Question

x^3-2x^2-5x+6 factorise​

Answer 1

Answer:

it is related to factor theorem

first write all factors of 6=+1,-1,+2,-2,+3,-3,+6,-6

now substitute each factor in place of x

by factor theorem

f(x)=1-2-5+6

therefore f(x)=0

therefore x-1 is a factor of this polynomial f(x)

Answer 2

x^3-2x^2-5x+6

Let f(x)=x^3-2x^2-5x+6

Let x=1

f(1)=1-2-5+6=0

So, (x-1) is a factor of x^3-2x^2-5x+6.

divide x^3-2x^2-5x+6 by x-1.

=x^2-x-6

=(x+2)(x-3)

x^3-2x^2-5x+6

=(x-1)(x+2)(x-3)