Question

show that(x-2)is a factor of 3x^2-x-10,hence, factorise 3x^2-x10.​

Answer 1

Answer:  (x−2)(3x+5)

Step-by-step explanation: Let

p(x)=3x  ^2  −x−10  and g(x)=x−2

To prove :  g(x) is a factor of p(x)

Proof : 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)