Question

how to fractorise using factor theorem??

Answer 1

How do l factorise x3−3x2−9x−5x3−3x2−9x−5 by using factor theorem?


answer :


notice, x=−1x=−1 satisfies the cubic equation: x3−3x2−9x−5=0x3−3x2−9x−5=0 hence from factor theorem, x+1x+1 is a factor of x3−3x2−9x−5x3−3x2−9x−5

∴x3−3x2−9x−5∴x3−3x2−9x−5

=x2(x+1)−4x(x+1)−5(x+1)=x2(x+1)−4x(x+1)−5(x+1)

=(x+1)(x2−4x−5)=(x+1)(x2−4x−5)

=(x+1)(x2−5x+x−5)=(x+1)(x2−5x⏟+x−5⏟)

=(x+1)(x(x−5)+(x−5))=(x+1)(x(x−5)+(x−5))

=(x+1)(x−5)(x+1)=(x+1)(x−5)(x+1)

=(x−5)(x+1)2