Q2 of 86 Page 48

Use the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:

f(x) = x3 – 4x2 + x + 6, g(x) = x – 2

By Factor Theorem, we know that,


If p(x) is a polynomial and a is any real number, then g(x) = (x – a) is a factor of p(x), if p(a) = 0


For checking (x – 2) to be a factor, we will find f(2)


⇒ f(2) = (2)3 – 4(2)2 + (2) + 6


⇒ f(–1) = 8 – 16 + 2 + 6


⇒ f(–1) = 0


As, f(–1) is equal to zero, therefore, g(x) = (x – 2) is a factor of f(x)


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