Question

factorise the above given question

Answer 1

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

2x3−3x2−5x+62x3-3x2-5x+6

Factor.

(x−2)(2x2+x−3)(x-2)(2x2+x-3)


Factor by grouping.


For a polynomial of the form ax2+bx+cax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅−3=−6a⋅c=2⋅-3=-6and whose sum is b=1b=1.



(x−2)(2x2−2x+3x−3)(x-2)(2x2-2x+3x-3)

Factor out the greatest common factor from each group.



Group the first two terms and the last two terms.

(x−2)((2x2−2x)+(3x−3))(x-2)((2x2-2x)+(3x-3))

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, x−1x-1.

(x−2)((x−1)(2x+3))(x-2)((x-1)(2x+3))

Remove unnecessary parentheses.

(x−2)(x−1)(2x+3)