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Practice Solutions

Factor completely.

$(- 5 x + 5 y) (3 x^{2} + 16 x - 12)$
$- 5 (x - y) (3 x - 2) (x + 6)$

$4 x^{2} - 100 y^{2}$
$4 (x^{2} - 25 y^{2}) 4 (x - 5 y) (x + 5 y)$

$3 x^{2} - 18 x - 48$
$3 (x^{2} - 6 x - 16) 3 (x - 8) (x + 2)$

$3 x^{3} + 4 x^{2} - 3 x - 4$
$(3 x^{3} + 4 x^{2}) + (- 3 x - 4) x^{2} (3 x + 4) - 1 (3 x + 4) (3 x + 4) (x^{2} - 1) (3 x + 4) (x - 1) (x + 1)$

$- 6 x^{2} y - 24 x y^{2} - 24 y^{3}$

$- 6 y (x^{2} + 4 x y + 4 y^{2}) - 6 y (x + 2 y) (x + 2 y) - 6 y {(x + 2 y)}^{2}$

$30 x^{3} - 190 x^{2} + 60 x$
$10 x (3 x^{2} - 19 x + 6) 10 x (3 x - 1) (x - 6)$

Factor completely.

$24 x^{2} - 54 x - 15$
$3 (8 x^{2} - 18 x - 5) 3 (4 x + 1) (2 x - 5)$

$12 x^{3} + 20 x^{2} - 3 x - 5$
$(12 x^{3} + 20 x^{2}) + (- 3 x - 5) 4 x^{2} (3 x + 5) - 1 (3 x + 5) (3 x + 5) (4 x^{2} - 1) (3 x + 5) (2 x - 1) (2 x + 1)$

$x^{3} - 8 x^{2} + 16 x$
$x (x^{2} - 8 x + 16) x (x - 4) (x - 4) x {(x - 4)}^{2}$

$4 x^{3} + 2 x^{2} - 36 x - 18$
$2 (2 x^{3} + x^{2} - 18 x - 9) 2 ((2 x^{3} + x^{2}) + (- 18 x - 9)) 2 (x^{2} (2 x + 1) - 9 (2 x + 1)) 2 (2 x + 1) (x^{2} - 9) 2 (2 x + 1) (x - 3) (x + 3)$

$28 x^{2} - 28 x y + 21 x - 21 y$
$7 (4 x^{2} - 4 x y + 3 x - 3 y) 7 ((4 x^{2} - 4 x y) + (3 x - 3 y)) 7 (4 x (x - y) + 3 (x - y)) 7 (x - y) (4 x + 3)$

$60 x^{2} - 80 x - 15$
$5 (12 x^{2} - 16 x - 3) 5 (2 x - 3) (6 x + 1)$