1 Pure Mathematics

Let $p(x) = 12x^3 - 8x^2 - 3x + 2$ .

a.

Prove that $(2 x - 1)$ is a factor of $p (x)$ .

[2]

b.

Factorise $p (x)$ completely.

[3]

c.

Prove that there are no real solutions to the equation

\frac{12 \sec^2 \theta + 2 \cos \theta}{3} = \frac{8}{3} \sec \theta + 1

[4]

Let $p(x) = 12x^3 - 8x^2 - 3x + 2$ .

a.

Prove that $(2 x - 1)$ is a factor of $p (x)$ .

[2]

b.

Factorise $p (x)$ completely.

[3]

c.

Prove that there are no real solutions to the equation

\frac{12 \sec^2 \theta + 2 \cos \theta}{3} = \frac{8}{3} \sec \theta + 1

[4]

1 Pure Mathematics Questions