Find the value of a, if x + 1 is the factor of the polynomial x³ + ax² - x + 2?
- -2
- -1
- 3
- None of these
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
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