Factorise the given expression if (x + 2) and (x + 3) are factors x3 + ax + b, and we need to determine the values of ‘a’ and ‘b’. With values of a and b we have to factorize the given polynomial completely
ML Aggarwal Avichal Publication, Factorisation, chapter 6, question no 23
Given polynomial is p(x)=x3+ax+b
x+2 is a factor
⇒ −2 is a root of the polynomial.
⇒(−2)3+a(−2)+b=0
⇒−2a+b=8
x+3 is a factor
⇒−3 is a root of the polynomial.
⇒(−3)3+a(−3)+b=0
⇒−3a+b=27
Solving the above equations,
we get a=−19, b=−30