The factor theoremAQA A-Level Maths: Mind map

Exam questions on The factor theorem

1. Let $f(x)=2x^3-x^2-7x+6$.
   Given that $(x-1)$ and $(2x-3)$ are factors of $f(x)$, factorise $f(x)$ completely.2 marks
2. The polynomial $p(x)=x^3+kx^2-4x+12$ has $(x-2)$ as a factor, where $k$ is a constant.
   Using your value of $k$, solve $p(x)=0$.2 marks
3. The cubic $g(x)=2x^3+ax^2+bx-12$, where $a$ and $b$ are constants, has factors $(x-2)$ and $(x+3)$.
   Use the factor theorem to show that $2a+b=-2$ and $3a-b=22$.3 marks