Algebraic Methods

$f(x) = 4x^3 - 8x^2 - 35x + 75$

a.

Use the factor theorem to show that $(x + 3)$ is a factor of $f (x)$ .

[2]

b.

Hence, show that $f (x)$ can be written in the form $f(x) = (x + 3)(ax + b)^2$ , where $a\,$ and $b\,$ are integers to be found.

[4]

$f(x) = 4x^3 - 8x^2 - 35x + 75$

a.

Use the factor theorem to show that $(x + 3)$ is a factor of $f (x)$ .

[2]

b.

Hence, show that $f (x)$ can be written in the form $f(x) = (x + 3)(ax + b)^2$ , where $a\,$ and $b\,$ are integers to be found.

[4]

Algebraic Methods Questions