Yulia

2020-12-24

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although $20{x}^{3}$ appears in both $20{x}^{3}+8{x}^{2}and20{x}^{3}+10x$, I’ll need to factor $20{x}^{3}$ in different ways to obtain each polynomial’s factorization?

### Answer & Explanation

Velsenw

Step 1
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although $20{x}^{3}$ appears in both $20{x}^{3}+8{x}^{2}$ and $20{x}^{3}+10x$, 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.

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