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Question
If x + 1 is a factor of the polynomial 2x3 + ax2 + 4x + 1, then a = ______.
Fill in the Blanks
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Solution
If x + 1 is a factor of the polynomial 2x3 + ax2 + 4x + 1, then a = 5.
Explanation:
If x + 1 is a factor, the polynomial must equal 0 at x = –1 (factor theorem).
Evaluate: 2(–1)3 + a(–1)2 + 4(–1) + 1
= –2 + a – 4 + 1
= a – 5
Set a – 5 = 0, so a = 5.
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