Q2 of 47 Page 80

Determine whether (x + 4) is a factor of x3 + 3x2 – 5x + 36.

Let f(x) = x3 + 3x2 – 5x + 36.

By factor theorem,


x + 4 = 0: x = – 4


If f(– 4) = 0, then (x + 4) is a factor


∴f(– 4) = (– 4)3 + 3(– 4)2 – 5(– 4) + 36


= – 64 + 48 + 20 + 36


= – 64 + 104 = 40


∴f(– 4) is not equal to 0


So, (x + 4) is not a factor of f(x).


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