How do you factor completely: $2 x^{7} + 10 x^{5} - 28 x^{3}$ $2x^7+10x^5-28x^3$ ?

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How do you factor completely: $2 x^{7} + 10 x^{5} - 28 x^{3}$ $2x^7+10x^5-28x^3$ ?

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Answer 1 · 2015-07-24T03:31:15

Factor: $2 x^{7} + 10 x^{5} - 28 x^{3}$ $2x^7 + 10x^5 - 28x^3$

Explanation:

$f (x) = 2 x^{3} (x^{4} + 5 x - 14) . C a l X = x^{2}$ $f(x) = 2x^3(x^4 + 5x - 14). Cal X = x^2$
$f (x) = 2 x^{3} (X^{2} + 5 X - 14) .$ $f(x) = 2x^3 (X^2 + 5X - 14).$
Factor the quadratic expression f(X) in the parentheses.
Find 2 numbers knowing sum (5) and product (-14).
They are: -2 and 5.
$f (X) = (X - 2) (X + 5) = (x^{2} - 2) (x^{2} + 5) = (x - \sqrt{2}) (x + \sqrt{2}) (x^{2} + 5)$ $f(X) = (X - 2)(X + 5) = (x^2 - 2)(x^2 + 5) = (x - sqrt2)(x + sqrt2)(x^2 + 5)$
Finally,
$f (x) = 2 x^{3} (x - \sqrt{2}) (x + \sqrt{2}) (x^{2} + 5)$ $f(x) = 2x^3(x - sqrt2)(x + sqrt2)(x^2 + 5)$

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How do you factor completely: $2 x^{7} + 10 x^{5} - 28 x^{3}$ $2x^7+10x^5-28x^3$ ?

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