1.5 Factoring polynomials  (Page 4/6)

If the terms of a polynomial do not have a GCF, does that mean it is not factorable? Explain.

A polynomial is factorable, but it is not a perfect square trinomial or a difference of two squares. Can you factor the polynomial without finding the GCF?

How do you factor by grouping?

$14x+4xy-18x{y}^2$

$49m{b}^2-35m^{2}ba+77m{a}^2$

$30x^{3}y-45x^2{y}^2+135x{y}^3$

$200p^3{m}^3-30p^2{m}^3+40m^3$

$36j^4{k}^2-18j^3{k}^3+54j^2{k}^4$

$6y^4-2y^3+3y^2-y$

$6x^2+5x-4$

$2a^2+9a-18$

$6c^2+41c+63$

$6n^2-19n-11$

$20w^2-47w+24$

$2p^2-5p-7$

$7x^2+48x-7$

$10h^2-9h-9$

$2b^2-25b-247$

$9d^2\mathrm{-73}d+8$

$90v^2\mathrm{-181}v+90$

$12t^2+t-13$

$2n^2-n-15$

$16x^2-100$

$25y^2-196$

$121p^2-169$

$4m^2-9$

$361d^2-81$

$324x^2-121$

$144b^2-25c^2$

$16a^2-8a+1$

$49n^2+168n+144$

$121x^2-88x+16$

$225y^2+120y+16$

$m^2-20m+100$

$m^2-20m+100$

$36q^2+60q+25$

$x^3+216$

$27y^3-8$

$125a^3+343$

$b^3-8d^3$

$64x^3\mathrm{-125}$

$729q^3+1331$

$125r^3+\mathrm{1,728}{s}^3$

$4x{\left(x-1\right)}^{-\frac{2}{3}}+3{\left(x-1\right)}^{\frac{1}{3}}$

$3c{\left(2c+3\right)}^{-\frac{1}{4}}-5{\left(2c+3\right)}^{\frac{3}{4}}$

$3t{\left(10t+3\right)}^{\frac{1}{3}}+7{\left(10t+3\right)}^{\frac{4}{3}}$

$14x{\left(x+2\right)}^{-\frac{2}{5}}+5{\left(x+2\right)}^{\frac{3}{5}}$

$9y{(3y-13)}^{\frac{1}{5}}-2{(3y-13)}^{\frac{6}{5}}$

$5z{(2z-9)}^{-\frac{3}{2}}+11{(2z-9)}^{-\frac{1}{2}}$

$6d{\left(2d+3\right)}^{-\frac{1}{6}}+5{\left(2d+3\right)}^{\frac{5}{6}}$

Factor by grouping to find the length and width of the park.

A statue is to be placed in the center of the park. The area of the base of the statue is $4x^2+12x+9{\text{m}}^2.$ Factor the area to find the lengths of the sides of the statue.

At the northwest corner of the park, the city is going to install a fountain. The area of the base of the fountain is $9x^2-25{\text{m}}^2.$ Factor the area to find the lengths of the sides of the fountain.

Find the length of the base of the flagpole by factoring.

$16x^4-200x^2+625$

$81y^4-256$

$16z^4-\mathrm{2,401}{a}^4$

$5x{\left(3x+2\right)}^{-\frac{2}{4}}+{\left(12x+8\right)}^{\frac{3}{2}}$

${(32x^3+48x^2-162x-243)}^{\mathrm{-1}}$