stop2dance3l

2021-12-10

Factor completely each polynomial, and indicate any that are not factorable using integers. $2{n}^{3}+6{n}^{2}+10n$

Kindlein6h

Step 1
Given the polynomial
$2{n}^{3}+6{n}^{2}+10n$
This has to be completely factorized.
The rule used here is
${a}^{m+n}={a}^{m}{a}^{2}$
Step 2
The factorization will be
$2{n}^{3}+6{n}^{2}+10n=2{n}^{2+1}+6{n}^{1+1}+10n$
$=2{n}^{2}n+6nn+10n$
$=2n\left({n}^{2}+3n+5\right)$
It cannot be factored further using integers.

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