Simplify (6a^2+10a+4)÷(3a+1)

Math
(6a2+10a+4)÷(3a+1)
Rewrite the division as a fraction.
6a2+10a+43a+1
Simplify the numerator.
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Factor 2 out of 6a2+10a+4.
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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.
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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.
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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.
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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)

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