How do you factor $15 x^{4} - 50 x^{3} - 40 x^{2}$ $15x^4-50x^3-40x^2$ ?

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How do you factor $15 x^{4} - 50 x^{3} - 40 x^{2}$ $15x^4-50x^3-40x^2$ ?

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Answer 1 · 2016-05-25T19:47:09

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

Explanation:

Look for the greatest common factors of all the numbers/letters. in this case, $5$ $5$ is common to $15$ $15$ , $50$ $50$ , and $40$ $40$ , and $x^{2}$ $x^2$ for the $x$ $x$ 's giving you:

$5 x^{2} (3 x^{2} - 10 x - 8)$ $5x^2 (3x^2 - 10x - 8)$

Since you have a number greater than $1$ $1$ for the $x^{2}$ $x^2$ inside the brackets, you can factor it further by determining what two number add up to $- 10$ $-10$ and multiply to $- 24$ $-24$ (derived from $3 \times (- 8)$ $3 xx (-8)$ ).

$4$ $4$ and $6$ $6$ won't work because of the negative numbers, however, $- 12$ $-12$ and $2$ $2$ will.

$5 x^{2} (3 x^{2} - 12 x + 2 x - 8)$ $5x^2 ( 3x^2 - 12x + 2x - 8)$

Look for the GCFs in the first two variables inside the brackets and then the second two.

$5 x^{2} [(3 x (x - 4) + 2 (x - 4)]$ $5x^2 [ ( 3x (x - 4) + 2 (x - 4) ]$

Collect like terms and simplify

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

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How do you factor $15 x^{4} - 50 x^{3} - 40 x^{2}$ $15x^4-50x^3-40x^2$ ?

1 Answer

Explanation:

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How do you factor $15 x^{4} - 50 x^{3} - 40 x^{2}$ $15x^4-50x^3-40x^2$ ?