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Question

Factors of (2x2−3x−2)(2x2−3x)−63 are:

A
(x3)(2x+3)(x1)(x7)
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B
(x+3)(2x+3)(x1)(x7)
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C
(x+3)(2x+3)(2x23x+7)
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D
(x3)(2x+3)(2x23x+7)
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Solution

The correct option is D (x3)(2x+3)(2x23x+7)
(2x23x2)(2x23x)63
=4x46x34x26x3+9x2+6x63
=4x412x3+5x2+15x+21x63
=4x3(x3)+5x(x3)+21(x3)
=(x3)(4x3+5x+21)
=(x3)(4x3+6x2+14x6x29x+21)
=(x3)(2x2(2x+3)3x(2x+3)+7(2x+3))
=(x3)(2x+3)(2x23x+7)

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