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)