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

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

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Answer 1 · 2015-05-27T18:10:15

$2 n^{2} + 5 n + 2$ $2n^2+5n+2$

coefficient of the first term: $2 = 2 \times 1$ $2 = 2xx1$
coefficient of the last term: $2 = 2 \times 1$ $2 = 2xx1$
coefficient of the middle term (using only the factors above): $5 = 2 \times 2 + 1 \times 1$ $5 = 2xx2+1xx1$

$2 n^{2} + 5 n + 2 = (2 n + 1) (n + 2)$ $2n^2+5n+2 = (2n+1)(n+2)$

Alternative method:
Treat the given expression as a quadratic set equal to zero, with the form
$a n^{2} + b n + c$ $an^2+bn+c$
and use the quadratic formula
$\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $(-b+-sqrt(b^2-4ac))/(2a)$
This will given solutions
$n = - 2$ $n=-2$ and $n = - \frac{1}{2}$ $n=-1/2$
for a factoring
$2 (n + 2) (n + \frac{1}{2})$ $2(n+2)(n+1/2)$

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

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