8a2-30a-274a+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=8⋅-27=-216 and whose sum is b=-30.

Factor -30 out of -30a.

8a2-30(a)-274a+3

Rewrite -30 as 6 plus -36

8a2+(6-36)a-274a+3

Apply the distributive property.

8a2+6a-36a-274a+3

8a2+6a-36a-274a+3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(8a2+6a)-36a-274a+3

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

2a(4a+3)-9(4a+3)4a+3

2a(4a+3)-9(4a+3)4a+3

Factor the polynomial by factoring out the greatest common factor, 4a+3.

(4a+3)(2a-9)4a+3

(4a+3)(2a-9)4a+3

Cancel the common factor.

(4a+3)(2a-9)4a+3

Divide 2a-9 by 1.

2a-9

2a-9

Divide (8a^2-30a-27)/(4a+3)