How do you factor $56 x^{3} + 70 x^{2} - 280 x - 350$ $56x^3+70x^2-280x-350$ ?

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How do you factor $56 x^{3} + 70 x^{2} - 280 x - 350$ $56x^3+70x^2-280x-350$ ?

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Answer 1 · 2016-04-26T21:43:32

$56 x^{3} + 70 x^{2} - 280 x - 350 = 14 (x - \sqrt{5}) (x + \sqrt{5}) (4 x + 5)$ $56x^3+70x^2-280x-350=14(x-sqrt(5))(x+sqrt(5))(4x+5)$

Explanation:

Separate out the common scalar factor $14$ $14$ , factor by grouping and finally use the difference of squares identity:

$a^{2} - b^{2} = (a - b) (a + b)$ $a^2-b^2=(a-b)(a+b)$

with $a = x$ $a=x$ and $b = \sqrt{5}$ $b=sqrt(5)$ as follows:

$56 x^{3} + 70 x^{2} - 280 x - 350$ $56x^3+70x^2-280x-350$

$= 14 (4 x^{3} + 5 x^{2} - 20 x - 25)$ $=14(4x^3+5x^2-20x-25)$

$= 14 ((4 x^{3} + 5 x^{2}) - (20 x + 25))$ $=14((4x^3+5x^2)-(20x+25))$

$= 14 (x^{2} (4 x + 5) - 5 (4 x + 5))$ $=14(x^2(4x+5)-5(4x+5))$

$= 14 (x^{2} - 5) (4 x + 5)$ $=14(x^2-5)(4x+5)$

$= 14 (x^{2} - {(\sqrt{5})}^{2}) (4 x + 5)$ $=14(x^2-(sqrt(5))^2)(4x+5)$

$= 14 (x - \sqrt{5}) (x + \sqrt{5}) (4 x + 5)$ $=14(x-sqrt(5))(x+sqrt(5))(4x+5)$

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How do you factor $56 x^{3} + 70 x^{2} - 280 x - 350$ $56x^3+70x^2-280x-350$ ?

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How do you factor $56 x^{3} + 70 x^{2} - 280 x - 350$ $56x^3+70x^2-280x-350$ ?