Find the value of a, if x + 1 is the factor of the polynomial x³ + ax² - x + 2?

Find the value of a, if x + 1 is the factor of the polynomial x³ + ax² - x + 2?

Explanation

Given that x + 1 is a factor of the polynomial x³ + ax² - x + 2, we know that (-1) is a root of the polynomial.

Let's plug in x = -1 into the polynomial:

(-1)³ + a(-1)² - (-1) + 2 = 0

-1 + a + 1 + 2 = 0

a + 2 = 0

Subtract 2 from both sides:

a = -2