Is (x + 7) a factor of f(x) = x3 − 3x2 + 2x − 8? Use either the remainder theorem or the factor theorem to explain your reasoning.

x + 7 is not a factor of the cubic polynomial

Step-by-step explanation:

Here, we want to find out if the linear equation is a factor of the cubic polynomial

To know this, we can simply set the linear equation to zero, then substitute the value into the polynomial

If the linear expression is a factor, then what we should have after substituting is zero

This is the remainder theorem

thus;

x + 7 = 0

x = -7

Substitute x = -7

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

-343 - 147 - 14 -8

The addition of all this is certainly not zero

So x + 7 is not a factor of the polynomial