Mathematics
Factorise the following:
(x2 - 3x)(x2 - 3x + 7) + 10
Factorisation
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Answer
Let us assume, x2 - 3x = t.
∴ (x2 - 3x)(x2 - 3x + 7) + 10 = t(t + 7) + 10
= t2 + 7t + 10
= t2 + 5t + 2t + 10
= t(t + 5) + 2(t + 5)
= (t + 5)(t + 2)
= (x2 - 3x + 5)(x2 - 3x + 2)
= (x2 - 3x + 5)(x2 - 2x - x + 2)
= (x2 - 3x + 5)[x(x - 2) - 1(x - 2)]
= (x2 - 3x + 5)(x - 2)(x - 1).
Hence, (x2 - 3x)(x2 - 3x + 7) + 10 = (x2 - 3x + 5)(x - 2)(x - 1).
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