Determine whether the statement makes sense or does not make sense, and explain your reasoning....

William Curry

William Curry

Answered

2021-12-29

Determine whether the statement makes sense or does not make sense, and explain your reasoning.
Although 20x3 appears in both 20x3+8x2 and 20x3+10x ,I’ll need to factor 20x3 in different ways to obtain each polynomial’s factorization.

Answer & Explanation

Paul Mitchell

Paul Mitchell

Expert

2021-12-30Added 40 answers

Step 1
Given:
20x3+8x2 and 20x3+10x
Step 2
Yes! statement makes sense
20x3+8x2
Break terms:
=2x×2x×5x+2x×2x×2
Take common out:
=2x×2x(5x+2)
=4x2(5x+2)
Step 3
20x3+10x
Take common out:
=10x(2x2+1)
SlabydouluS62

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 20x3
Vasquez

Vasquez

Expert

2022-01-09Added 457 answers

The statement makes sense because polynomials have a different greatest common factors. Hence, 20x3 will be factored differently.
In the first polynomial the greatest common factor is 4x2. Hence, we factor it out:
20x3+8x2=4x2(5x+2)
In the second polynomial the greatest common factor is 10x so, we factor it out:
20x3+10x=10x(x2+1)
Result:
It makes sence.

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