2×2-5x+3×2+5x-6

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅3=6 and whose sum is b=-5.

Factor -5 out of -5x.

2×2-5(x)+3×2+5x-6

Rewrite -5 as -2 plus -3

2×2+(-2-3)x+3×2+5x-6

Apply the distributive property.

2×2-2x-3x+3×2+5x-6

2×2-2x-3x+3×2+5x-6

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2×2-2x)-3x+3×2+5x-6

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

2x(x-1)-3(x-1)x2+5x-6

2x(x-1)-3(x-1)x2+5x-6

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

(x-1)(2x-3)x2+5x-6

(x-1)(2x-3)x2+5x-6

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -6 and whose sum is 5.

-1,6

Write the factored form using these integers.

(x-1)(2x-3)(x-1)(x+6)

(x-1)(2x-3)(x-1)(x+6)

Cancel the common factor.

(x-1)(2x-3)(x-1)(x+6)

Rewrite the expression.

2x-3x+6

2x-3x+6

Simplify (2x^2-5x+3)/(x^2+5x-6)