1fully worked

Is $(x-3)$ a factor of $f(x)=x^{3}-4x^{2}+3x$?

1$(x-3)$ means substitute $x=3$Read off the value to substitute (watch the sign)

2$f(3)=27-36+9=0$Substitute and evaluate

3yes, it is a factorState whether it is a factor

Check - Why substitute $3$ and not $-3$?

A $(x-3)$ is zero when $x=3$B because $3$ is positiveC you should use $-3$D either works

2you finish it

Is $(x+2)$ a factor of $f(x)=x^{3}+2x^{2}-x-2$?

1$(x+2)$ means substitute $x=-2$Read off the value to substitute (watch the sign)

2$f(-2)=-8+8+2-2=0$Substitute and evaluate

3State whether it is a factor

Check - What would a non-zero answer have told you?

A it is not a factor, and the value is the remainderB you made an errorC it is still a factorD nothing

3you finish it

Is $(x-1)$ a factor of $f(x)=x^{3}+2x^{2}+3$?

1$(x-1)$ means substitute $x=1$Read off the value to substitute (watch the sign)

2Substitute and evaluate

3State whether it is a factor

Check - What is the remainder when $f(x)$ is divided by $(x-1)$?

A $0$B $6$C $1$D $3$

4you do it all

$(x-2)$ is a factor of $x^{3}+kx^{2}-4$. Find $k$.

1Read off the value to substitute (watch the sign)

2Substitute and evaluate

3State whether it is a factor

Check - Why can you set the expression equal to zero?

A a factor means the polynomial vanishes at that valueB because $k$ is unknownC you cannotD because $-4$ is negative