Question

check whether the polynomial g(x) is a factor of f(x) or not in the following f(x) = x3 - 3x2 + 5x -2, g(x) = x/2+1/3​

Answer 1

>>Maths

>>Polynomials

>>Factorisation of Polynomial

>>Use the Factor Theorem to determine whet3

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

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

Solution

Given polynomial f(x)=x3+3x2+3x+1 and g(x)=x+1

If x+1 is factor then f(−1)=0

Replace x in  p(x) by −1 we get

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

or,f(−1)=(−1)3+3(−1)2+3(−1)+1

or,f(−1)=−1+3−3+1

or,f(−1)=0

So g(x)=x+1 is factor of  f(x)=x3+3x2+3x+1