Question

Is (x + 2) a factor of x + 6x2 + 3x – 10?

Answer 1

Answer:

no

Step-by-step explanation:

6x² + 4x - 10 in factored form is:

2(3x+5)(x-1)

Answer 2

Answer:

Assuming that you actually mean that if $(x+2)$ is a factor of $x^{3}+6x^{2}+3x-10$, the answer is yes.

Step-by-step explanation:

We need to do long division of the polynomial to figure out if this is true. I would show it here, but it is extremely difficult to do so. (Maybe someone could help me.) When I factor it, it does not leave a remainder, so this is true.

$x^{3}+6x^{2}+3x-10= (x+2)(x^2+4x-5)$

Another way one could figure this out is by graphing the equation $x^{3}+6x^{2}+3x-10$ on your graphing calculator or on just a graphing website, lake Desmos. The screenshot below shows the graph.

The polynomial will have a factor of $(x-c)$ if the point $(0,c)$ exists on the graph. The graph has the following three zeroes.

$(0,-2)$, $(0, -5)$, and $(0,1)$

As such, it has the three factors $(x-(-2))$, $(x-(-5))$, and $(x-1)$.

Since $(x-(-2)=(x+2)$, it is a factor of the polynomial.