An important question from factorisation chapter for examination as it has been already asked in previous year paper of 2014 in which we asked to factorise the following polynomial: x3+10x2−37x+26 using factor and remainder theorem
ML Aggarwal Avichal Publication chapter 6, question no 17
Let f(x)=x3+10x2−37x+26
Putting x=1,
we get
f(1)=1+10−37+26=0
∴ By factor theorem, x−1 is factor of f(x).
On dividing x3+10x2−37x+26 by x−1,
we get x2+11x−26 as the quotient and remainder =0.
∴ The other factor of f(x) are the factor of x2+11x−26
Now, x2+11x−26
=x2+13x−2x−26
=x(x+13)−2(x+13)
=(x+13)(x−2)
Hence, x3+10x2−37x+26=(x−1)(x−2)(x+13)