Mathematics
Factorise the following:
(2x2 + 5x)(2x2 + 5x - 19) + 84
Factorisation
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Answer
Let 2x2 + 5x = y then,
(2x2 + 5x)(2x2 + 5x - 19) + 84 = y(y - 19) + 84.
= y2 - 19y + 84
= y2 - 12y - 7y + 84
= y(y - 12) - 7(y - 12)
= (y - 12)(y - 7)
= (2x2 + 5x - 12)(2x2 + 5x - 7).
Factorising 2x2 + 5x - 12 we get,
2x2 + 5x - 12 = 2x2 + 8x - 3x - 12
= 2x(x + 4) - 3(x + 4)
= (2x - 3)(x + 4).
Factorising 2x2 + 5x - 7 we get,
2x2 + 5x - 7 = 2x2 + 7x - 2x - 7
= x(2x + 7) - 1(2x + 7)
= (2x + 7)(x - 1).
Hence, (2x2 + 5x)(2x2 + 5x - 19) + 84 = (2x - 3)(x + 4)(2x + 7)(x - 1).
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