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Factoring completely. If polynomial is not factorable, write prime.


1.) 21x^3-18x^2y+ 24xy^2
2.) a^2+ 7a-18
3.) b^2 +8b + 7
4..) 4f^2-64
5.) 9x^2 + 25
6.) 8j^3k-4jk^3-7
8.) 2ak- 6a+k-3
9.)y^2+18y+81



Answer :

[tex]1)\ 21x^3-18x^2y+24xy^2=3x(7x^2-6xy+8y^2)\\\\2)\ a^2+7a-18=a^2+9a-2a-18=a(a+9)-2(a+9)\\=(a+9)(a-2)\\\\3)\ b^2+8b+7=b^2+b+7b+7=b(b+1)+7(b+1)\\=(b+1)(b+7)\\\\4)\ 4f^2-64=4(f^2-16)=4(f^2-4^2)=4(f-4)(f+4)\\\\5)\ 9x^2+25-not\ factorable[/tex]

[tex]6)\ 8j^3k-4jk^3-7-not\ factorable\\\\8)\ 2ak-6a+k-3=2a(k-3)+1(k-3)=(k-3)(2a+1)\\\\9)\ y^2+18y+81=y^2+2y\cdot9+9^2=(y+9)^2=(y+9)(y+9)[/tex]