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Find the value of a for which (x - a) is a factor of the polynomial x³ - a² x + x + 2.
- -1
- 1
- 2
- -2
Correct answer: -2
Solution
By the factor theorem, P(a) = 0. Substitute x = a: a³ - a²*a + a + 2 = a³ - a³ + a + 2 = a + 2. Set a + 2 = 0 => a = -2. Let me re-check: a³ - a²(a) + a + 2 = a³ - a³ + a + 2 = a + 2 = 0 => a = -2. So the correct value is a = -2.
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