(6a2+10a+4)÷(3a+1)

Rewrite the division as a fraction.

6a2+10a+43a+1

Factor 2 out of 6a2+10a+4.

Factor 2 out of 6a2.

2(3a2)+10a+43a+1

Factor 2 out of 10a.

2(3a2)+2(5a)+43a+1

Factor 2 out of 4.

2(3a2)+2(5a)+2(2)3a+1

Factor 2 out of 2(3a2)+2(5a).

2(3a2+5a)+2(2)3a+1

Factor 2 out of 2(3a2+5a)+2(2).

2(3a2+5a+2)3a+1

2(3a2+5a+2)3a+1

Factor by grouping.

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

Factor 5 out of 5a.

2(3a2+5(a)+2)3a+1

Rewrite 5 as 2 plus 3

2(3a2+(2+3)a+2)3a+1

Apply the distributive property.

2(3a2+2a+3a+2)3a+1

2(3a2+2a+3a+2)3a+1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

2((3a2+2a)+3a+2)3a+1

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

2(a(3a+2)+1(3a+2))3a+1

2(a(3a+2)+1(3a+2))3a+1

Factor the polynomial by factoring out the greatest common factor, 3a+2.

2((3a+2)(a+1))3a+1

2(3a+2)(a+1)3a+1

2(3a+2)(a+1)3a+1

Simplify (6a^2+10a+4)÷(3a+1)