Polynomials & Factor Theorem Practice Questions

Work out $f(1)$.

Show that $(x - 2)$ is a factor of $f(x)$.

Solve $(3x + 2)(x - 4)(x + 1) = 0$

$g(x)$ is a polynomial and $g(-5) = 0$

Write down a linear factor of $g(x)$.

Fully factorise $2x^3 + 3x^2 - 11x - 6$

$(2x + 5)$ is a factor of $2x^3 - x^2 - 23x - 20$

Work out the other two linear factors.

Solve $4x^3 + 12x^2 = 7x$

Show that $(2x - 1)$ is a factor of $f(x)$.

Is $(x - 3)$ a factor of $f(x)$?

You must show your working.

Work out the value of $a$.

Hence fully factorise $6x^3 + ax^2 - 7x - 6$ using your value of $a$.

Show that $V = 4x^3 - 64x^2 + 240x$

The volume of the box is $256$ cm$^3$

Show that $x^3 - 16x^2 + 60x - 64 = 0$

Work out the possible values of $x$.

Give your answers as exact values and give a reason for rejecting any value you do not use.

Show that $2p + q = -16$

Work out the value of $p$ and the value of $q$.

Hence solve $f(x) = 0$