William Curry

Answered

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.

Although

Answer & Explanation

Paul Mitchell

Expert

2021-12-30Added 40 answers

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:

$=2x\times 2x\times 5x+2x\times 2x\times 2$

Take common out:

$=2x\times 2x(5x+2)$

$=4{x}^{2}(5x+2)$

Step 3

$20{x}^{3}+10x$

Take common out:

$=10x(2{x}^{2}+1)$

Given:

Step 2

Yes! statement makes sense

Break terms:

Take common out:

Step 3

Take common out:

SlabydouluS62

Expert

2021-12-31Added 52 answers

The statement

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

makes sense because the two polynomials each contain another term which has a different common factor with

Vasquez

Expert

2022-01-09Added 457 answers

The statement makes sense because polynomials have a different greatest common factors. Hence,

In the first polynomial the greatest common factor is

In the second polynomial the greatest common factor is 10x so, we factor it out:

Result:

It makes sence.

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