6.4 General Strategy for Factoring Polynomials

Factor completely: $7 x^{3} - 21 x^{2} - 70 x .$

Factor completely: $8 y^{3} + 16 y^{2} - 24 y .$

Factor completely: $5 y^{3} - 15 y^{2} - 270 y .$

Factor completely: $24 y^{2} - 150 .$

Factor completely: $16 x^{3} - 36 x .$

Factor completely: $27 y^{2} - 48 .$

Factor completely: $4 a^{2} - 12 a b + 9 b^{2} .$

Factor completely: $4 x^{2} + 20 x y + 25 y^{2} .$

Factor completely: $9 x^{2} - 24 x y + 16 y^{2} .$

Factor completely $12 x^{3} y^{2} + 75 x y^{2} .$

Factor completely: $50 x^{3} y + 72 x y .$

Factor completely: $27 x y^{3} + 48 x y .$

Factor completely: $250 m^{3} + 432 n^{3} .$

Factor completely: $2 p^{3} + 54 q^{3} .$

Factor completely: $3 x^{5} y - 48 x y .$

Factor completely: $4 a^{5} b - 64 a b .$

Factor completely: $7 x y^{5} - 7 x y .$

Factor completely: $4 x^{2} + 8 b x - 4 a x - 8 a b .$

Factor completely: $6 x^{2} - 12 x c + 6 b x - 12 b c .$

Factor completely: $16 x^{2} + 24 x y - 4 x - 6 y .$

Factor completely: $40 x^{2} y + 44 x y - 24 y .$

Factor completely: $4 p^{2} q - 16 p q + 12 q .$

Factor completely: $6 p q^{2} - 9 p q - 6 p .$

Factor completely: $9 x^{2} - 12 x y + 4 y^{2} - 49 .$

Factor completely: $4 x^{2} - 12 x y + 9 y^{2} - 25 .$

Factor completely: $16 x^{2} - 24 x y + 9 y^{2} - 64 .$

Factor completely.

$2 n^{2} + 13 n - 7$

Factor completely.

$a^{5} + 9 a^{3}$

Factor completely.

$121 r^{2} - s^{2}$

Factor completely.

$8 m^{2} - 32$

Factor completely.

$25 w^{2} - 60 w + 36$

Factor completely.

$m^{2} + 14 m n + 49 n^{2}$

Factor completely.

$7 b^{2} + 7 b - 42$

Factor completely.

$3 x^{4} y - 81 x y$

Factor completely.

$k^{4} - 16$

Factor completely.

$5 x^{5} y^{2} - 80 x y^{2}$

Factor completely.

$15 p q - 15 p + 12 q - 12$

Factor completely.

$4 x^{2} + 40 x + 84$

Factor completely.

$4 u^{5} + 4 u^{2} v^{3}$

Factor completely.

$4 c^{2} + 20 c d + 81 d^{2}$

Factor completely.

$10 m^{4} - 6250$

Factor completely.

$36 x^{2} y + 15 x y - 6 y$

Factor completely.

$8 x^{3} - 27 y^{3}$

Factor completely.

$y^{6} - 1$

Factor completely.

$9 x^{2} - 6 x y + y^{2} - 49$

Factor completely.

$\left(3 x + 1\right)^{2} - 6 \left(3 x + 1\right) + 9$

Explain what it mean to factor a polynomial completely.

Of all the factoring methods covered in this chapter (GCF, grouping, undo FOIL, ‘ac’ method, special products) which is the easiest for you? Which is the hardest? Explain your answers.