Question

Using the factor theorem, which of the following is a factor of the polynomial below?

Answer 1

ANSWER

The correct choice is D.

EXPLANATION

Let

$f( x) = 3 {x}^{3} - 4 {x}^{2} - 13x - 6$

According to the Factor Theorem, if x-a is a factor of f(x), then f(a)=0.

For option A,

$f( - 6) = 3 {( - 6)}^{3} - 4 {( - 6)}^{2} - 13( - 6) - 6$

$f( - 6) = - 720$

Hence x+6 is not a factor.

For option B,

$f( - 3) = 3 {( - 3)}^{3} - 4 {( - 3)}^{2} - 13( - 3) - 6$

$f( - 3) = - 84$

x+3 is also not a factor.

For option C,

$f( 4) = 3 {( 4)}^{3} - 4 {( 4)}^{2} - 13( 4) - 6$

$f(4) = 70$

Option D,

$f( - 1) = 3 {( - 1)}^{3} - 4 {( - 1)}^{2} - 13( - 1) - 6$

$f( - 1) = - 3 - 4 + 13 - 6$

$f( - 1) = 0$

x+1 is a factor.