Charles Kingsley

2021-12-17

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although $20{x}^{3}$ appears in both , I’ll need to factor $20{x}^{3}$ in different ways to obtain each polynomial’s factorization?

vicki331g8

Step 1
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although $20{x}^{3}$ appears in both , I’ll need to factor $20{x}^{3}$ in different ways to obtain each polynomial’s factorization?
Step 2
We are given two expressions:
$20{x}^{3}+8{x}^{2}$
and $20{x}^{3}+10x$
if we factorize them,
$20{x}^{3}+8{x}^{2}=4{x}^{2}\left(5x+2\right)$
and $20{x}^{3}+10x=10x\left(2{x}^{2}+1\right)$
We see that factorization depends on each term of the expression, so although both expressions contain one common term, because of the other term both have different ways.

ol3i4c5s4hr

Step 1
Given:
$20{x}^{3}+8{x}^{2}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}20{x}^{3}+10x$
Step 2
Yes! statement makes sense
$20{x}^{3}+8{x}^{2}$
Break terms:
$=2x×2x×5x+2x×2x×2$
Take common out:
$=2x×2x\left(5x+2\right)$
$=4{x}^{2}\left(5x+2\right)$
Step 3
$20{x}^{3}+10x$
Take common out:
$=10x\left(2{x}^{2}+1\right)$

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