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Question

Given that a±12, simplify the expression 2a2+5a34a21?

A
2a32a+1
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B
a32a1
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C
2a+32a1
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D
a+32a+1
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Solution

The correct option is D a+32a+1
We need to simplify 2a2+5a34a21
On factoring, we get
= 2a21a+6a3
= a(2a1)+3(2a1)
The factors are (2a1)(a+3)
4a21=(2a1)(2a+1)
2a2+5a34a21=(2a1)(a+3)(2a1)(2a+1)
= a+32a+1

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