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Question
Factorise by substituting terms:
6(x + 2)2 – 5(x + 2) – 4
Sum
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Solution
Given expression: 6(x + 2)2 – 5(x + 2) – 4
We have to find two numbers whose sum is –5 and whose product is –24.
These numbers are –8 and 3.
Now, using middle term factorisation method,
6(x + 2)2 – 5(x + 2) – 4
= 6(x + 2)2 – 8(x + 2) + 3(x + 3) – 4
= 2(x + 2) [3(x + 2) – 4] + [3(x + 2) – 4]
= [3(x + 2) – 4] [2(x + 2) + 1]
= (3x + 6 – 4) (2x + 4 + 1)
= (3x + 2) (2x + 5)
The factorisation result is (3x + 2) (2x + 5).
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