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) = 5x3 + x2 – 5x – 1, g(x) = x + 1

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+1) to be a factor, we will find f(–1)


⇒ f(–1) = 5 (–1)3 + (–1)2 – 5(–1) – 1


⇒ f(–1) = –5 + 1 + 5 – 1


⇒ f(–1) = 0


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


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