How do you factor $2 x^{3} + 5 x^{2} + 2 x$ $2x^3+5x^2+2x$ ?

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Answer 1 · 2015-05-16T15:14:42

$f (x) = x (2 x^{2} + 5 x + 2)$ $f(x) = x(2x^2 + 5x + 2)$
Factor the trinomial in parentheses by the new AC method.

Converted trinomial: f'(x) = 2x^2 + 5x + 4 = (x - p')(x - q')

Product ac = 4. Sum (1 + 4) = 5.= b. The numbers are: p' = 1 and q' = 4.

Then, $p = (p')/a = 1/2$ , and $q = (q')/a = 4/2 = 2$

$f(x) = x(x + 1/2)(x + 2) = x(2x + 1)(x + 2)$

Check by developing.
$f(x) = x(2x^2 + 4x + x + 2) = x(2x^2 + 5x + 2).$ OK

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