What is the quotient when (x+3) is divided into the polynomial 2x2+3x-9

Problem: 2x^2+3x-9

For a polynomial of the form, ax^2+bx+c rewrite the middle term as the sum of two terms whose product a·c=2·-9=-18 and whose sum is b=3.

Factor 3 out of 3x

2x^2+3 (x) - 9

Rewrite 3 as - 3 plus 6.

2x^2 + (-3+6) x-9

Apply the distributive property

2x^2 (-3x+6x) - 9

Remove the parentheses

2x^2-3x+6x-9

Factor out the greatest common factor from each group

Group the first two terms and the last two terms

(2x^2-3x) (6x-9)

Factor out the greatest common factor in each group.

x (2x-3) + 3 (2x-3)

Factor the polynomial by factoring out the greatest common factor, 2x-3

(x+3) (2x-3). So, the quotient is 2x-3