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Question
Factorize the following polynomial.
(x – 5)2 – (5x – 25) – 24
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Solution
(x – 5)2 – (5x – 25) – 24
= (x – 5)2 – 5(x – 5) – 24
Let x – 5 = z
∴ (x – 5)2 – 5 (x – 5) – 24
= z2 – 5z – 24
= z2 – 8z + 3z – 24
= z (z – 8) + 3 (z – 8)
= (z – 8) (z + 3)
= (x – 5 – 8) (x – 5 + 3) (Replace z = x - 5)
= (x – 13) (x – 2)
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