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Question
Factors of 4 + 4x – x2 – x3 are ______.
Options
(2 + x)(2 – x)(1 + x)
(x – 2)(1 + x)(2 + x)
(x + 2)(x – 2)(1 – x)
(2 + x)(x – 1)(2 – x)
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Solution
Factors of 4 + 4x – x2 – x3 are (2 + x)(2 – x)(1 + x).
Explanation:
4 + 4x – x2 – x3 = 4(1 + x) – x2(1 + x)
= (1 + x)(4 – x2)
= (1 + x)(22 – x2) ...[∵ a2 – b2 = (a – b)(a + b)]
= (1 + x)(2 – x)(2 + x)
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