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Question
Factorize the following polynomial.
(x2 – 2x + 3) (x2 – 2x + 5) – 35
Solution
(x2 – 2x + 3) (x2 – 2x + 5) – 35
Let x2 – 2x = z
∴ (x2 - 2x + 3) (x2 - 2x + 5) - 35
= (z + 3) (z + 5) - 35
= z2 + 5z + 3z + 15 - 35
= z2 + 8z - 20
= z2 + 10z - 2z - 20
= z (z + 10) - 2 (z + 10)
= (z + 10) (z - 2)
= (x2 - 2x + 10) (x2 - 2x - 2) (Replace z = x2 - 2x)
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