Answer:
Assuming that you actually mean that if [tex](x+2)[/tex] is a factor of [tex]x^{3}+6x^{2}+3x-10[/tex], 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.
[tex]x^{3}+6x^{2}+3x-10= (x+2)(x^2+4x-5)[/tex]
Another way one could figure this out is by graphing the equation [tex]x^{3}+6x^{2}+3x-10[/tex] 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 [tex](x-c)[/tex] if the point [tex](0,c)[/tex] exists on the graph. The graph has the following three zeroes.
[tex](0,-2)[/tex], [tex](0, -5)[/tex], and [tex](0,1)[/tex]
As such, it has the three factors [tex](x-(-2))[/tex], [tex](x-(-5))[/tex], and [tex](x-1)[/tex].
Since [tex](x-(-2)=(x+2)[/tex], it is a factor of the polynomial.
