Show that (x – 2) is a factor of 3x 2 −x−10. Hence, factories 3x 2 −x−10

0

A basic question from factorisation chapter in which we are asked to prove that (x – 2) is a factor of 3x2−x−10. It means ultimately we have to factories 3x2−x−10

ML Aggarwal Avichal Publication, Factorisation, chapter 6, Question no 10

Consider g(x)=0⇒x−2=0⇒x=2

Now putting x=2 in p(x), We get

p(2)=3(2)

2

−(2)−10

=12−2−10=0

∴ By factor theorem, (x−2) is a factor of p(x)

Hence proved.

Now, 3x

2

−x−10

=3x

2

−6x+5x−10

=3x(x−2)+5(x−2)

=(x−2)(3x+5)