Is (x + 7) a factor of f(x) = x^3 − 3x^2 + 2x − 8? Use either the remainder theorem or the factor theorem to explain your reasoning.

Step-by-step explanation:

I don't think so. 7 is not a factor of 8, but let's try it and see.

x = - 7

f(-7) = (-7)^3 - 3(-7)^2 + 2(-7) + 8

f(-7) = -343 - 3(49)  + 14 + 8

f(-7) = -484

The graph shows that the x intercept (the one you are interested in) takes place at a little over 3. The calculation shows that when x = -7, the y value is -484 which is nowhere's near 0.

No there is a remainder of -512

Step-by-step explanation:

Divide (x+7) into (x^3 - 3x^2 + 2x - 8)

x^2-10x+72 R -512/(x+7)