1.1.10 Algebra and functions

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

a.

Prove that $(2 x - 3)$ is a factor of $L (x)$ .

[2]

b.

Factorise $L (x)$ completely.

[3]

c.

Prove that there are no real solutions to the equation

\frac{2 \sin^2 \phi + 12 \csc \phi}{4} = \frac{3}{4} \sin \phi + 2

[4]

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

a.

Prove that $(2 x - 3)$ is a factor of $L (x)$ .

[2]

b.

Factorise $L (x)$ completely.

[3]

c.

Prove that there are no real solutions to the equation

\frac{2 \sin^2 \phi + 12 \csc \phi}{4} = \frac{3}{4} \sin \phi + 2

[4]

1.1.10 Algebra and functions Questions