Question

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

Answer 1

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) \\eq 0`, so we can say that
`(x + 2)` is not a factor

Answer 2

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...