Question

Is (x+2) a factor of 3x^3-2x^2-4

Answer 1

IF (x+2) is a factor of the equation, when x=-2, the equation will equal zero...(because the factor equals zero and the equation is the product of its factors and zero times anything is zero.)

3(-2)^3-2(-2)^2-4

-24-8-4=-36

So (x+2) is not a factor...

Answer 2

Recall the Factor theorem.
"A polynomial $f(x)$ has a factor $(x - k)$ if and only if $f(k) = 0$"

Thus, let's convert that into what we know here.
$f(x) = 3x^{3} - 2x^{2} - 4$
A polynomial $f(x)$ has a factor $(x - (-2))$ if and only if $f(-2) = 0$

So, let's substitute -2 in place of x.

$f(-2) = 3(-2)^{3} - 2(-2)^{2} - 4 = -36$

But $f(-2) \neq 0$, so we can say that $(x + 2)$ is not a factor