Question

Explain how you can determine whether (x + 1) is a factor of P(x) = x³ + 3x² - 6x - 7 without actually dividing. Then determine if it is a factor.

Answer 1

Step-by-step explanation:

We can use the following theorem:

Theorem: If (x + a) is a factor of P(x), then P(-a) = 0.

In other words, if we substitute -a for x in P(x), and we get 0, then (x + a) is a factor of P(x).

In this case, we have P(x) = x³ + 3x² - 6x - 7. Substituting -1 for x, we get:

P(-1) = (-1)³ + 3(-1)² - 6(-1) - 7 = -1 + 3 + 6 - 7 = 0

Therefore, (x + 1) is a factor of P(x)