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How do you factor $15 x^{4} - 39 x^{3} + 18 x^{2}$ $15x^4-39x^3+18x^2$ ?

1 Answer

Jul 25, 2017

$= 3 x^{2} (x - 2) (5 x - 3)$ $=3x^2(x-2)(5x-3)$

Explanation:

Take out a common factor of $3 x^{2}$ $3x^2$ first:

$15 x^{4} - 39 x^{3} + 18 x^{2}$ $15x^4 -39x^3 +18x^2$

$= 3 x^{2} (5 x^{2} - 13 x + 6)$ $=3x^2(5x^2 -13x+6)$

Find factors of $5 and 6$ $5 and 6$ whose products ADD to $13$ $13$

$5 and 6$ $" "5" and "6$
$↓ \times \times ↓$ $" "darrcolor(white)(xxxx)darr$

$1 \times \times x 2 \to 5 \times 2 = 10$ $" "1 color(white)(xxxxx)2" "rarr 5 xx 2 = 10$
$" "5color(white)(xxxxx)3" "rarr 1xx3 = ul3$
$color(white)(xxxxxxxxxxxxxxxxxxx)13$

These are the correct factors: the signs in both brackets will be $-$

$=3x^2(5x^2 -13x+6)$

$=3x^2(x-2)(5x-3)$

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