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Question
If x + α is a factor of the polynomial 2x2 + 2αx + 4x + 12, then α = ______.
Fill in the Blanks
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Solution
If x + α is a factor of the polynomial 2x2 + 2αx + 4x + 12, then α = 3.
Explanation:
The polynomial is 2x2 + (2α + 4)x + 12. If x + α is a factor, set x = –α and equate to zero:
2(–α)2 + (2α + 4)(–α) + 12 = 0
⇒ 2α2 – 2α2 – 4α + 12 = 0
⇒ –4α + 12 = 0
⇒ α = 3
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