Factor Theorem · MCQ assessment

Version A

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 - x^2 + x + 1$.
Work out $f(1)$.

A1B-2C2D3

2$f(x) = x^3 - 3x^2 - x - 9$.
Work out $f(3)$.

A-9B-15C-12D12

3$f(x) = x^3 - 2x^2 - 4x + 6$.
Work out $f(3)$.

A0B-3C3D6

4$f(x) = x^3 + 4x^2 - 6x - 7$.
Work out $f(-2)$.

A11B15C-13D13

5$f(x) = x^3 - 2x^2 + 2x - 3$.
Work out $f(3)$.

A12B9C15D-12

6$(x + 1)$ is a factor of $f(x) = x^3 - x^2 - 5x + k$, where $k$ is a constant.
Find the value of $k$.

A2B-3C-4D3

7Find the remainder when $f(x) = x^3 - 2x^2 + 2x - 5$ is divided by $(x - 1)$.

A-4B-3C-10D4

8Which of these is a factor of $f(x) = x^3 - 3x^2 - 10x + 24$?

A$(x - 1)$B$(x + 4)$C$(x + 3)$D$(x + 1)$

9$(x + 3)$ is a factor of $f(x) = x^3 + x^2 + 2x + k$, where $k$ is a constant.
Find the value of $k$.

A25B-24C24D22

10Find the remainder when $f(x) = x^3 - 2x^2 + 4x + 2$ is divided by $(x + 3)$.

A55B-58C23D-55

11Which of these is a factor of $f(x) = x^3 + 5x^2 - 2x - 24$?

A$(x - 3)$B$(x - 1)$C$(x + 3)$D$(x - 5)$

12The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x - 3)(x - 2)(x + 3)$B$(x - 3)(x + 2)(x - 3)$C$(x + 3)(x + 2)(x - 3)$D$(x - 3)(x - 2)(x - 3)$

13Solve $x^3 - 6x^2 + 5x + 12 = 0$, given that $(x + 1)$ is a factor.

A$x = -4,\ -3,\ -1$B$x = -1,\ 3,\ 4$C$x = -1,\ 3$D$x = -4,\ -3,\ 1$

14Solve $x^3 - x^2 - 14x + 24 = 0$, given that $(x + 4)$ is a factor.

A$x = -3,\ -2,\ 4$B$x = -4,\ -3,\ -2$C$x = -4,\ 2$D$x = -4,\ 2,\ 3$

15Solve $x^3 + 4x^2 + x - 6 = 0$, given that $(x + 3)$ is a factor.

A$x = -1,\ 2,\ 3$B$x = -3,\ -2,\ 1$C$x = -3,\ -1,\ 2$D$x = -3,\ -2$

How confident do you feel on this topic now?RedAmberGreen

Factor Theorem · MCQ assessment

Version B

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 + 2x^2 - 6x + 9$.
Work out $f(-1)$.

A17B16C15D-16

2$f(x) = x^3 - 4x^2 - x + 9$.
Work out $f(-3)$.

A51B-48C-54D-51

3$f(x) = x^3 - 2x^2 - 2x + 5$.
Work out $f(-3)$.

A-31B-34C-37D34

4$f(x) = x^3 - 2x^2 + 2x - 6$.
Work out $f(1)$.

A-6B-5C5D-4

5$f(x) = x^3 - 5x^2 - x - 9$.
Work out $f(-1)$.

A14B-14C-15D-13

6Find the remainder when $f(x) = x^3 + 2x^2 + 3x - 3$ is divided by $(x + 1)$.

A5B3C-6D-5

7$(x - 2)$ is a factor of $f(x) = x^3 - 4x^2 - 5x + k$, where $k$ is a constant.
Find the value of $k$.

A18B-18C14D23

8Which of these is a factor of $f(x) = x^3 - x^2 - 16x + 16$?

A$(x + 1)$B$(x + 3)$C$(x - 3)$D$(x - 4)$

9Find the remainder when $f(x) = x^3 - 2x^2 - 2x - 7$ is divided by $(x + 1)$.

A-10B-8C8D-9

10$(x - 3)$ is a factor of $f(x) = x^3 + x^2 + 5x + k$, where $k$ is a constant.
Find the value of $k$.

A-50B-56C-51D51

11Which of these is a factor of $f(x) = x^3 + 9x^2 + 26x + 24$?

A$(x - 3)$B$(x - 2)$C$(x + 3)$D$(x + 5)$

12Solve $x^3 + 4x^2 + x - 6 = 0$, given that $(x + 3)$ is a factor.

A$x = -3,\ -2$B$x = -3,\ -2,\ 1$C$x = -1,\ 2,\ 3$D$x = -3,\ -1,\ 2$

13The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x - 3)(x - 1)(x - 3)$B$(x + 3)(x + 1)(x - 3)$C$(x - 3)(x + 1)(x - 3)$D$(x - 3)(x - 1)(x + 3)$

14Solve $x^3 + 2x^2 - 11x - 12 = 0$, given that $(x + 4)$ is a factor.

A$x = -4,\ -1,\ 3$B$x = -4,\ -1$C$x = -4,\ -3,\ 1$D$x = -3,\ 1,\ 4$

15Solve $x^3 + 5x^2 + 2x - 8 = 0$, given that $(x + 4)$ is a factor.

A$x = -4,\ -2,\ 1$B$x = -4,\ -1,\ 2$C$x = -1,\ 2,\ 4$D$x = -4,\ -2$

How confident do you feel on this topic now?RedAmberGreen

Factor Theorem · MCQ assessment

Version C

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 - 4x^2 - x + 7$.
Work out $f(1)$.

A2B3C-3D4

2$f(x) = x^3 + 4x^2 - 3x - 3$.
Work out $f(-1)$.

A2B4C3D-3

3$f(x) = x^3 + 4x^2 - 2x - 8$.
Work out $f(1)$.

A-6B5C-4D-5

4$f(x) = x^3 + 5x^2 - 2x - 6$.
Work out $f(1)$.

A-3B-1C-2D2

5$f(x) = x^3 + 5x^2 - 3x + 6$.
Work out $f(-2)$.

A26B-24C22D24

6$(x + 1)$ is a factor of $f(x) = x^3 - x^2 + 3x + k$, where $k$ is a constant.
Find the value of $k$.

A5B2C-5D4

7Which of these is a factor of $f(x) = x^3 + 2x^2 - 5x - 6$?

A$(x - 2)$B$(x + 5)$C$(x - 4)$D$(x - 5)$

8Find the remainder when $f(x) = x^3 + 3x^2 + x + 4$ is divided by $(x + 1)$.

A5B9C4D-5

9$(x + 1)$ is a factor of $f(x) = x^3 - 2x^2 + 6x + k$, where $k$ is a constant.
Find the value of $k$.

A7B-9C9D3

10Which of these is a factor of $f(x) = x^3 - 4x^2 - 4x + 16$?

A$(x + 5)$B$(x + 3)$C$(x - 5)$D$(x + 2)$

11Find the remainder when $f(x) = x^3 - x^2 - 3x - 2$ is divided by $(x - 3)$.

A-7B7C-29D10

12The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x + 2)(x + 1)(x - 1)$B$(x - 2)(x - 1)(x - 1)$C$(x + 2)(x - 1)(x - 1)$D$(x - 2)(x - 1)(x + 1)$

13Solve $x^3 - 5x^2 + 2x + 8 = 0$, given that $(x + 1)$ is a factor.

A$x = -4,\ -2,\ 1$B$x = -4,\ -2,\ -1$C$x = -1,\ 2,\ 4$D$x = -1,\ 2$

14Solve $x^3 - 6x^2 + 11x - 6 = 0$, given that $(x - 1)$ is a factor.

A$x = -3,\ -2,\ 1$B$x = 1,\ 2,\ 3$C$x = -3,\ -2,\ -1$D$x = 1,\ 2$

15Solve $x^3 + x^2 - 10x + 8 = 0$, given that $(x + 4)$ is a factor.

A$x = -4,\ -2,\ -1$B$x = -2,\ -1,\ 4$C$x = -4,\ 1,\ 2$D$x = -4,\ 1$

How confident do you feel on this topic now?RedAmberGreen

Factor Theorem · MCQ assessment

Version D

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 - 3x^2 - x + 4$.
Work out $f(3)$.

A1B4C-2D-1

2$f(x) = x^3 + 5x^2 - 4x - 8$.
Work out $f(1)$.

A-5B-7C6D-6

3$f(x) = x^3 + x^2 + 5x - 3$.
Work out $f(-1)$.

A8B-8C-7D-9

4$f(x) = x^3 - x^2 - x + 4$.
Work out $f(3)$.

A22B-19C16D19

5$f(x) = x^3 - 5x^2 - 6x - 1$.
Work out $f(2)$.

A25B-25C-23D-27

6Find the remainder when $f(x) = x^3 + 3x^2 + 3x + 7$ is divided by $(x - 1)$.

A6B15C-14D14

7Which of these is a factor of $f(x) = x^3 - 2x^2 - 5x + 6$?

A$(x - 2)$B$(x - 3)$C$(x - 4)$D$(x + 4)$

8$(x + 2)$ is a factor of $f(x) = x^3 - x^2 + 4x + k$, where $k$ is a constant.
Find the value of $k$.

A16B20C19D-20

9Find the remainder when $f(x) = x^3 + x^2 + x - 2$ is divided by $(x + 3)$.

A23B-23C37D-26

10Which of these is a factor of $f(x) = x^3 + 8x^2 + 19x + 12$?

A$(x + 2)$B$(x - 2)$C$(x - 3)$D$(x + 1)$

11$(x - 2)$ is a factor of $f(x) = x^3 + 2x^2 + 5x + k$, where $k$ is a constant.
Find the value of $k$.

A-26B-31C26D-24

12Solve $x^3 - 3x^2 - 10x + 24 = 0$, given that $(x + 3)$ is a factor.

A$x = -4,\ -2,\ 3$B$x = -4,\ -3,\ -2$C$x = -3,\ 2,\ 4$D$x = -3,\ 2$

13The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x - 3)(x + 1)(x - 2)$B$(x - 3)(x - 1)(x + 2)$C$(x + 3)(x + 1)(x - 2)$D$(x - 3)(x - 1)(x - 2)$

14Solve $x^3 + 4x^2 + x - 6 = 0$, given that $(x + 3)$ is a factor.

A$x = -3,\ -2,\ 1$B$x = -3,\ -2$C$x = -1,\ 2,\ 3$D$x = -3,\ -1,\ 2$

15Solve $x^3 - 6x^2 + 5x + 12 = 0$, given that $(x + 1)$ is a factor.

A$x = -4,\ -3,\ -1$B$x = -4,\ -3,\ 1$C$x = -1,\ 3$D$x = -1,\ 3,\ 4$

How confident do you feel on this topic now?RedAmberGreen

Factor Theorem · MCQ assessment

Version E

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 + 5x^2 - 5x - 8$.
Work out $f(3)$.

A49B46C-49D52

2$f(x) = x^3 - 2x^2 + 3x - 8$.
Work out $f(1)$.

A-6B-5C-7D6

3$f(x) = x^3 + 4x^2 + 5x + 2$.
Work out $f(1)$.

A13B12C11D-12

4$f(x) = x^3 - 5x^2 - 4x + 2$.
Work out $f(-3)$.

A-58B58C-55D-61

5$f(x) = x^3 - 3x^2 - x - 2$.
Work out $f(-1)$.

A-4B-6C5D-5

6$(x - 2)$ is a factor of $f(x) = x^3 + 2x^2 + 2x + k$, where $k$ is a constant.
Find the value of $k$.

A20B-20C-22D-18

7Which of these is a factor of $f(x) = x^3 - 6x^2 + 5x + 12$?

A$(x - 2)$B$(x + 5)$C$(x - 3)$D$(x - 1)$

8Find the remainder when $f(x) = x^3 + 5x^2 + x - 4$ is divided by $(x - 1)$.

A-1B4C3D-3

9$(x - 2)$ is a factor of $f(x) = x^3 + 2x^2 - 3x + k$, where $k$ is a constant.
Find the value of $k$.

A-7B10C-10D-8

10Which of these is a factor of $f(x) = x^3 - 4x^2 + x + 6$?

A$(x + 2)$B$(x + 1)$C$(x - 5)$D$(x + 3)$

11Find the remainder when $f(x) = x^3 + x^2 + 3x + 9$ is divided by $(x - 2)$.

A-27B-1C29D27

12The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x - 2)(x - 1)(x + 1)$B$(x + 2)(x - 1)(x - 1)$C$(x - 2)(x - 1)(x - 1)$D$(x + 2)(x + 1)(x - 1)$

13Solve $x^3 - 5x^2 + 2x + 8 = 0$, given that $(x + 1)$ is a factor.

A$x = -1,\ 2$B$x = -1,\ 2,\ 4$C$x = -4,\ -2,\ -1$D$x = -4,\ -2,\ 1$

14Solve $x^3 - 9x^2 + 26x - 24 = 0$, given that $(x - 2)$ is a factor.

A$x = 2,\ 3,\ 4$B$x = -4,\ -3,\ 2$C$x = -4,\ -3,\ -2$D$x = 2,\ 3$

15Solve $x^3 - 2x^2 - 11x + 12 = 0$, given that $(x + 3)$ is a factor.

A$x = -4,\ -3,\ -1$B$x = -4,\ -1,\ 3$C$x = -3,\ 1,\ 4$D$x = -3,\ 1$

How confident do you feel on this topic now?RedAmberGreen

Factor Theorem · MCQ assessment

Version F

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 + 4x^2 + 4x + 5$.
Work out $f(2)$.

A-37B37C35D39

2$f(x) = x^3 + 3x^2 - 2x + 1$.
Work out $f(-2)$.

A7B-9C9D11

3$f(x) = x^3 - 4x^2 - x - 2$.
Work out $f(-2)$.

A-26B-22C24D-24

4$f(x) = x^3 - x^2 - x - 2$.
Work out $f(3)$.

A-13B10C13D16

5$f(x) = x^3 - 3x^2 - x + 5$.
Work out $f(3)$.

A5B2C-1D-2

6Find the remainder when $f(x) = x^3 - 2x^2 - 3x - 8$ is divided by $(x - 3)$.

A8B-5C-8D-44

7Which of these is a factor of $f(x) = x^3 + 6x^2 + 5x - 12$?

A$(x + 1)$B$(x - 2)$C$(x + 2)$D$(x + 4)$

8$(x + 3)$ is a factor of $f(x) = x^3 + 5x^2 - 2x + k$, where $k$ is a constant.
Find the value of $k$.

A-19B24C-22D-24

9Find the remainder when $f(x) = x^3 - x^2 + 6x + 4$ is divided by $(x - 1)$.

A-4B11C10D-10

10Which of these is a factor of $f(x) = x^3 + 6x^2 + 11x + 6$?

A$(x - 5)$B$(x + 2)$C$(x - 1)$D$(x + 5)$

11$(x - 1)$ is a factor of $f(x) = x^3 + 2x^2 + 5x + k$, where $k$ is a constant.
Find the value of $k$.

A-13B8C-8D-6

12Solve $x^3 - 3x^2 - 10x + 24 = 0$, given that $(x + 3)$ is a factor.

A$x = -3,\ 2$B$x = -3,\ 2,\ 4$C$x = -4,\ -3,\ -2$D$x = -4,\ -2,\ 3$

13The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x - 2)(x - 1)(x - 1)$B$(x - 2)(x - 1)(x + 1)$C$(x + 2)(x + 1)(x - 1)$D$(x + 2)(x - 1)(x - 1)$

14Solve $x^3 + 3x^2 - 10x - 24 = 0$, given that $(x + 4)$ is a factor.

A$x = -4,\ -2,\ 3$B$x = -4,\ -2$C$x = -4,\ -3,\ 2$D$x = -3,\ 2,\ 4$

15Solve $x^3 - 4x^2 + x + 6 = 0$, given that $(x + 1)$ is a factor.

A$x = -3,\ -2,\ -1$B$x = -1,\ 2$C$x = -3,\ -2,\ 1$D$x = -1,\ 2,\ 3$

How confident do you feel on this topic now?RedAmberGreen

Factor Theorem · MCQ assessment

Version G

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 - 2x^2 - x - 2$.
Work out $f(2)$.

A-4B-2C4D-6

2$f(x) = x^3 + 3x^2 - x + 5$.
Work out $f(-3)$.

A8B-8C11D5

3$f(x) = x^3 + 3x^2 + 3x + 2$.
Work out $f(-1)$.

A2B0C1D-1

4$f(x) = x^3 + x^2 - x + 8$.
Work out $f(3)$.

A38B41C44D-41

5$f(x) = x^3 + 4x^2 - 5x - 4$.
Work out $f(-3)$.

A17B23C20D-20

6Find the remainder when $f(x) = x^3 + x^2 + 4x - 7$ is divided by $(x + 2)$.

A-21B13C-19D19

7$(x + 1)$ is a factor of $f(x) = x^3 - x^2 + 6x + k$, where $k$ is a constant.
Find the value of $k$.

A-8B8C2D7

8Which of these is a factor of $f(x) = x^3 - 13x - 12$?

A$(x + 5)$B$(x + 2)$C$(x - 5)$D$(x + 3)$

9Find the remainder when $f(x) = x^3 - 3x^2 - 3x - 6$ is divided by $(x + 2)$.

A-20B-16C-22D20

10$(x - 1)$ is a factor of $f(x) = x^3 + 4x^2 + x + k$, where $k$ is a constant.
Find the value of $k$.

A6B-7C-6D-2

11Which of these is a factor of $f(x) = x^3 + 2x^2 - 5x - 6$?

A$(x + 2)$B$(x - 4)$C$(x - 5)$D$(x + 3)$

12Solve $x^3 - 3x^2 - 10x + 24 = 0$, given that $(x + 3)$ is a factor.

A$x = -4,\ -3,\ -2$B$x = -3,\ 2$C$x = -3,\ 2,\ 4$D$x = -4,\ -2,\ 3$

13The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x + 2)(x + 2)(x - 3)$B$(x + 2)(x - 2)(x - 3)$C$(x - 2)(x - 2)(x - 3)$D$(x - 2)(x + 2)(x + 3)$

14Solve $x^3 - 13x - 12 = 0$, given that $(x + 3)$ is a factor.

A$x = -3,\ -1$B$x = -4,\ 1,\ 3$C$x = -3,\ -1,\ 4$D$x = -4,\ -3,\ 1$

15Solve $x^3 + 8x^2 + 19x + 12 = 0$, given that $(x + 4)$ is a factor.

A$x = 1,\ 3,\ 4$B$x = -4,\ -3$C$x = -4,\ 1,\ 3$D$x = -4,\ -3,\ -1$

How confident do you feel on this topic now?RedAmberGreen

Factor Theorem · MCQ assessment

Version H

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 - x^2 + 2x + 7$.
Work out $f(-2)$.

A-7B-9C9D-11

2$f(x) = x^3 - 5x^2 + 3x + 3$.
Work out $f(-2)$.

A-31B-33C-29D31

3$f(x) = x^3 + 3x^2 + 6x - 5$.
Work out $f(-2)$.

A-13B-11C13D-15

4$f(x) = x^3 + 2x^2 - 6x + 9$.
Work out $f(2)$.

A15B-13C13D11

5$f(x) = x^3 + 3x^2 + 6x + 5$.
Work out $f(2)$.

A35B39C37D-37

6Find the remainder when $f(x) = x^3 + 3x^2 - 2x - 1$ is divided by $(x - 1)$.

A3B1C2D-1

7$(x - 3)$ is a factor of $f(x) = x^3 + 4x^2 - x + k$, where $k$ is a constant.
Find the value of $k$.

A-60B-56C60D-59

8Which of these is a factor of $f(x) = x^3 + 4x^2 - 9x - 36$?

A$(x + 5)$B$(x - 2)$C$(x - 1)$D$(x + 4)$

9Find the remainder when $f(x) = x^3 - 3x^2 + 2x - 6$ is divided by $(x + 3)$.

A66B-69C0D-66

10$(x - 1)$ is a factor of $f(x) = x^3 - 3x^2 - 6x + k$, where $k$ is a constant.
Find the value of $k$.

A14B-8C5D8

11Which of these is a factor of $f(x) = x^3 - 2x^2 - 11x + 12$?

A$(x + 2)$B$(x + 1)$C$(x - 4)$D$(x + 4)$

12Solve $x^3 - 2x^2 - 5x + 6 = 0$, given that $(x + 2)$ is a factor.

A$x = -2,\ 1,\ 3$B$x = -3,\ -1,\ 2$C$x = -3,\ -2,\ -1$D$x = -2,\ 1$

13The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x - 2)(x + 2)(x + 3)$B$(x + 2)(x - 2)(x - 3)$C$(x - 2)(x - 2)(x - 3)$D$(x + 2)(x + 2)(x - 3)$

14Solve $x^3 - 2x^2 - 11x + 12 = 0$, given that $(x + 3)$ is a factor.

A$x = -3,\ 1,\ 4$B$x = -4,\ -1,\ 3$C$x = -3,\ 1$D$x = -4,\ -3,\ -1$

15Solve $x^3 + 3x^2 - 6x - 8 = 0$, given that $(x + 4)$ is a factor.

A$x = -4,\ -2,\ 1$B$x = -4,\ -1,\ 2$C$x = -2,\ 1,\ 4$D$x = -4,\ -1$

How confident do you feel on this topic now?RedAmberGreen

Factor Theorem · MCQ assessment

Version I

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 + 2x^2 + 2x - 8$.
Work out $f(3)$.

A43B46C-43D40

2$f(x) = x^3 + 2x^2 + 6x + 3$.
Work out $f(-3)$.

A-24B24C-27D-21

3$f(x) = x^3 - 5x^2 - 2x - 8$.
Work out $f(-3)$.

A-71B74C-74D-77

4$f(x) = x^3 + 5x^2 - 5x - 6$.
Work out $f(-2)$.

A18B-16C14D16

5$f(x) = x^3 - 5x^2 - 2x + 3$.
Work out $f(-1)$.

A1B0C-2D-1

6Find the remainder when $f(x) = x^3 - x^2 + 4x + 4$ is divided by $(x - 1)$.

A-2B-8C9D8

7$(x + 3)$ is a factor of $f(x) = x^3 - 2x^2 + 6x + k$, where $k$ is a constant.
Find the value of $k$.

A61B-63C63D57

8Which of these is a factor of $f(x) = x^3 + 3x^2 - x - 3$?

A$(x - 2)$B$(x + 1)$C$(x + 5)$D$(x - 5)$

9Find the remainder when $f(x) = x^3 + 5x^2 - 3x - 9$ is divided by $(x + 1)$.

A2B-2C-3D-6

10$(x + 3)$ is a factor of $f(x) = x^3 - 2x^2 - 2x + k$, where $k$ is a constant.
Find the value of $k$.

A37B-39C41D39

11Which of these is a factor of $f(x) = x^3 - 4x^2 + x + 6$?

A$(x + 2)$B$(x - 2)$C$(x + 3)$D$(x - 1)$

12The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x - 3)(x + 1)(x + 2)$B$(x - 3)(x - 1)(x - 2)$C$(x - 3)(x + 1)(x - 2)$D$(x + 3)(x - 1)(x - 2)$

13Solve $x^3 - 7x + 6 = 0$, given that $(x + 3)$ is a factor.

A$x = -2,\ -1,\ 3$B$x = -3,\ 1,\ 2$C$x = -3,\ 1$D$x = -3,\ -2,\ -1$

14Solve $x^3 - 5x^2 - 2x + 24 = 0$, given that $(x + 2)$ is a factor.

A$x = -4,\ -3,\ -2$B$x = -2,\ 3,\ 4$C$x = -2,\ 3$D$x = -4,\ -3,\ 2$

15Solve $x^3 + 7x^2 + 14x + 8 = 0$, given that $(x + 4)$ is a factor.

A$x = -4,\ -2,\ -1$B$x = -4,\ -2$C$x = 1,\ 2,\ 4$D$x = -4,\ 1,\ 2$

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Factor Theorem · MCQ assessment

Version J

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1$f(x) = x^3 + 2x^2 - x + 9$.
Work out $f(3)$.

A-51B54C48D51

2$f(x) = x^3 - 5x^2 + 4x - 5$.
Work out $f(3)$.

A11B-11C-14D-8

3$f(x) = x^3 - 5x^2 + 5x + 5$.
Work out $f(-3)$.

A82B-82C-85D-79

4$f(x) = x^3 + 4x^2 + x - 5$.
Work out $f(1)$.

A1B2C0D-1

5$f(x) = x^3 + x^2 - 2x - 5$.
Work out $f(2)$.

A1B5C3D-3

6Find the remainder when $f(x) = x^3 - 3x^2 - x + 7$ is divided by $(x - 2)$.

A-11B-1C1D3

7$(x - 2)$ is a factor of $f(x) = x^3 - 2x^2 - 5x + k$, where $k$ is a constant.
Find the value of $k$.

A10B-10C8D15

8Which of these is a factor of $f(x) = x^3 - 3x^2 - 10x + 24$?

A$(x - 5)$B$(x - 3)$C$(x - 2)$D$(x - 1)$

9Find the remainder when $f(x) = x^3 + 5x^2 - 4x + 1$ is divided by $(x - 1)$.

A4B-3C9D3

10$(x + 3)$ is a factor of $f(x) = x^3 - 2x^2 + 6x + k$, where $k$ is a constant.
Find the value of $k$.

A63B61C-63D57

11Which of these is a factor of $f(x) = x^3 - 4x^2 - 4x + 16$?

A$(x + 5)$B$(x + 4)$C$(x - 1)$D$(x - 2)$

12The graph shows $y = f(x)$, a cubic that crosses the $x$-axis at the three marked points.
The coefficient of $x^3$ in $f(x)$ is $1$.
Write $f(x)$ as a product of three linear factors.

A$(x - 3)(x + 1)(x - 2)$B$(x - 3)(x - 1)(x - 2)$C$(x - 3)(x + 1)(x + 2)$D$(x + 3)(x - 1)(x - 2)$

13Solve $x^3 - 13x + 12 = 0$, given that $(x + 4)$ is a factor.

A$x = -4,\ 1,\ 3$B$x = -4,\ 1$C$x = -4,\ -3,\ -1$D$x = -3,\ -1,\ 4$

14Solve $x^3 - 6x^2 + 5x + 12 = 0$, given that $(x + 1)$ is a factor.

A$x = -1,\ 3,\ 4$B$x = -1,\ 3$C$x = -4,\ -3,\ -1$D$x = -4,\ -3,\ 1$

15Solve $x^3 + 6x^2 + 5x - 12 = 0$, given that $(x + 4)$ is a factor.

A$x = -4,\ -3$B$x = -1,\ 3,\ 4$C$x = -4,\ -3,\ 1$D$x = -4,\ -1,\ 3$

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