(5×2+13x-6)÷(x+3)

Rewrite the division as a fraction.

5×2+13x-6x+3

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=5⋅-6=-30 and whose sum is b=13.

Factor 13 out of 13x.

5×2+13(x)-6x+3

Rewrite 13 as -2 plus 15

5×2+(-2+15)x-6x+3

Apply the distributive property.

5×2-2x+15x-6x+3

5×2-2x+15x-6x+3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(5×2-2x)+15x-6x+3

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

x(5x-2)+3(5x-2)x+3

x(5x-2)+3(5x-2)x+3

Factor the polynomial by factoring out the greatest common factor, 5x-2.

(5x-2)(x+3)x+3

(5x-2)(x+3)x+3

Cancel the common factor.

(5x-2)(x+3)x+3

Divide 5x-2 by 1.

5x-2

5x-2

Divide (5x^2+13x-6)÷(x+3)