William Curry

2021-12-29

Determine whether the 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.

Paul Mitchell

Expert

Step 1
Given:
$20{x}^{3}+8{x}^{2}$ and $20{x}^{3}+10x$
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:
$=10x\left(2{x}^{2}+1\right)$

SlabydouluS62

Expert

The statement
makes sense because the two polynomials each contain another term which has a different common factor with $20{x}^{3}$

Vasquez

Expert

The statement makes sense because polynomials have a different greatest common factors. Hence, $20{x}^{3}$ will be factored differently.
In the first polynomial the greatest common factor is $4{x}^{2}$. Hence, we factor it out:
$20{x}^{3}+8{x}^{2}=4{x}^{2}\left(5x+2\right)$
In the second polynomial the greatest common factor is 10x so, we factor it out:
$20{x}^{3}+10x=10x\left({x}^{2}+1\right)$
Result:
It makes sence.

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