Factor 45q^2+57q+18

Math
45q2+57q+18
Factor 3 out of 45q2+57q+18.
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Factor 3 out of 45q2.
3(15q2)+57q+18
Factor 3 out of 57q.
3(15q2)+3(19q)+18
Factor 3 out of 18.
3(15q2)+3(19q)+3(6)
Factor 3 out of 3(15q2)+3(19q).
3(15q2+19q)+3(6)
Factor 3 out of 3(15q2+19q)+3(6).
3(15q2+19q+6)
3(15q2+19q+6)
Factor.
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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=15⋅6=90 and whose sum is b=19.
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Factor 19 out of 19q.
3(15q2+19(q)+6)
Rewrite 19 as 9 plus 10
3(15q2+(9+10)q+6)
Apply the distributive property.
3(15q2+9q+10q+6)
3(15q2+9q+10q+6)
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
3((15q2+9q)+10q+6)
Factor out the greatest common factor (GCF) from each group.
3(3q(5q+3)+2(5q+3))
3(3q(5q+3)+2(5q+3))
Factor the polynomial by factoring out the greatest common factor, 5q+3.
3((5q+3)(3q+2))
3((5q+3)(3q+2))
Remove unnecessary parentheses.
3(5q+3)(3q+2)
3(5q+3)(3q+2)
Factor 45q^2+57q+18

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