Let f(x) = x^3 -2x^2-29x-42. a)Show (x+2) is a factor b)Factorise f(x) completely
a) To show (x+2) is a factor, we want to show f(-2)=0. So (-2)^3-2(-2)^2 -29(-2)-42=-8-8+58-42=0
b) Divide x^3 -2x^2-29x-42 by x+2 to get x^2-4x-21 which we factorise to get (x+3)(x-7). Hence f(x)=(x+2)(x+3)(x-7)
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