Factor 12c^4+36c^3+15c^2

Math
12c4+36c3+15c2
Factor 3c2 out of 12c4+36c3+15c2.
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Factor 3c2 out of 12c4.
3c2(4c2)+36c3+15c2
Factor 3c2 out of 36c3.
3c2(4c2)+3c2(12c)+15c2
Factor 3c2 out of 15c2.
3c2(4c2)+3c2(12c)+3c2(5)
Factor 3c2 out of 3c2(4c2)+3c2(12c).
3c2(4c2+12c)+3c2(5)
Factor 3c2 out of 3c2(4c2+12c)+3c2(5).
3c2(4c2+12c+5)
3c2(4c2+12c+5)
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=4⋅5=20 and whose sum is b=12.
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Factor 12 out of 12c.
3c2(4c2+12(c)+5)
Rewrite 12 as 2 plus 10
3c2(4c2+(2+10)c+5)
Apply the distributive property.
3c2(4c2+2c+10c+5)
3c2(4c2+2c+10c+5)
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
3c2((4c2+2c)+10c+5)
Factor out the greatest common factor (GCF) from each group.
3c2(2c(2c+1)+5(2c+1))
3c2(2c(2c+1)+5(2c+1))
Factor the polynomial by factoring out the greatest common factor, 2c+1.
3c2((2c+1)(2c+5))
3c2((2c+1)(2c+5))
Remove unnecessary parentheses.
3c2(2c+1)(2c+5)
3c2(2c+1)(2c+5)
Factor 12c^4+36c^3+15c^2

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