Q. 2 B5.0( 6 Votes )

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

f(x) = x3 + 3x2 + 3x + 1, g(x) = x + 1

Answer :

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) = (–1)3 + 3(–1)2 + 3(–1) + 1


f(–1) = – 1 + 3 – 3 + 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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