1.2.10 Manipulating polynomials

Given that

P(x) = 64x^3 + 96x^2 + 44x + 6

a.

Use the factor theorem to prove that $(4 x + 1)$ is a factor of $P (x)$ .

[2]

b.

Factorise $P (x)$ completely.

[3]

c.

Hence, prove that $128n^3 + 192n^2 + 88n + 12$ is a multiple of 12 when $n$ is a positive whole number.

[4]

Given that

P(x) = 64x^3 + 96x^2 + 44x + 6

a.

Use the factor theorem to prove that $(4 x + 1)$ is a factor of $P (x)$ .

[2]

b.

Factorise $P (x)$ completely.

[3]

c.

Hence, prove that $128n^3 + 192n^2 + 88n + 12$ is a multiple of 12 when $n$ is a positive whole number.

[4]

1.2.10 Manipulating polynomials Questions