1.2.10 Manipulating polynomials

Let $f(x) = 6x^3 + 13x^2 - 4x - 15$ .

Use the factor theorem to show that $(2 x + 3)$ is a factor of $f (x)$ .

[2]

Hence, using algebra, write $f (x)$ as a product of three linear factors.

[3]

Solve, for $π2<θ<π\frac{\pi}{2} < \theta < \pi$ , the equation

6\tan^3 \theta + 13\tan^2 \theta - 4\tan \theta - 15 = 0

giving your answers to 3 significant figures.

[4]

1.2.10 Manipulating polynomials Questions

Let $f(x) = 6x^3 + 13x^2 - 4x - 15$ .

Use the factor theorem to show that $(2 x + 3)$ is a factor of $f (x)$ .

[2]

Hence, using algebra, write $f (x)$ as a product of three linear factors.

[3]

Solve, for $π2<θ<π\frac{\pi}{2} < \theta < \pi$ , the equation

6\tan^3 \theta + 13\tan^2 \theta - 4\tan \theta - 15 = 0

giving your answers to 3 significant figures.

[4]