Question

what binomial expressions are factors of

4x^3 + 9x^2 - x - 6

(multiple choice)

answers:

A. x - 2

b. x - 1

c. x + 1

d. x + 2

Answer 1

Answer: C and D

Step-by-step explanation:

The factor theorem tells us that if we evaluate a polynomial $p(x)$ at $x=a$ and the answer is 0, then $(x-a)$ is a factor of $p(x)$.

So we can check,

$x=2$ from $(x-2)$

$x=1$ from $(x-1)$

$x=-1$ from $(x+1)$

and

$x=-2$ from $(x+2)$

and see which gives us 0. For those that give 0, that respective expression is a factor of the binomial expression given.

• Substituting $x=2$ into $4x^{3}+9x^{2}-x-6$ gives us:

$4(2)^{3}+9(2)^{2}-(2)-6\\=60$

• Substituting $x=1$ into $4x^{3}+9x^{2}-x-6$ gives us:

$4(1)^{3}+9(1)^{2}-(1)-6\\=6$

• Substituting $x=-1$ into $4x^{3}+9x^{2}-x-6$ gives us:

$4(-1)^{3}+9(-1)^{2}-(-1)-6\\=0$

• Substituting $x=-2$ into $4x^{3}+9x^{2}-x-6$ gives us:

$4(-2)^{3}+9(-2)^{2}-(2)-6\\=0$

The last 2 gives us 0. Hence, $(x+1)$ and $(x+2)$ are factors of $4x^{3}+9x^{2}-x-6$. Answer choices C and D are correct.