Find the GCD of the following
x2 + 14x + 33, x3 + 10x2 – 11x
Given,
X2 + 14x + 33 = x2 + 3x + 11x + 33 = x(x + 3) + 11(x + 3)
= (x + 11)(x + 3)
X3 + 10x2 – 11x = x(x2 + 10x – 11) = x(x2 + 11x – x – 11)
= x[x(x + 11) – 1(x + 11)]
= x(x + 11)(x – 1)
Greatest common divisor = (x + 11)
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