Question
Find the greatest common divisor (GCD) of (x 2
- 9x + 14) and (x 2 + x - 56).Solution
(x 2 - 9x + 14) = x 2 - 7x - 2x + 14 = x(x - 7) - 2(x - 7) = (x - 7) (x - 2)
x 2 + x - 56 = x 2 + 8x - 7x - 56 = x(x + 8) - 7(x + 8) = (x - 7) (x + 8)
So, required GCD = (x - 7)
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