Factor 21m^4+19m^2n-12n^2

Math
21m4+19m2n-12n2
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=21⋅-12=-252 and whose sum is b=19.
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Reorder terms.
21m4-12n2+19m2n
Reorder -12n2 and 19m2n.
21m4+19m2n-12n2
Factor 19 out of 19m2n.
21m4+19(m2n)-12n2
Rewrite 19 as -9 plus 28
21m4+(-9+28)(m2n)-12n2
Apply the distributive property.
21m4-9(m2n)+28(m2n)-12n2
Remove unnecessary parentheses.
21m4-9m2n+28(m2n)-12n2
Remove unnecessary parentheses.
21m4-9m2n+28m2n-12n2
21m4-9m2n+28m2n-12n2
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(21m4-9m2n)+28m2n-12n2
Factor out the greatest common factor (GCF) from each group.
3m2(7m2-3n)+4n(7m2-3n)
3m2(7m2-3n)+4n(7m2-3n)
Factor the polynomial by factoring out the greatest common factor, 7m2-3n.
(7m2-3n)(3m2+4n)
Factor 21m^4+19m^2n-12n^2

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