Question

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

Polynomial factorization
ANSWERED
asked 2020-12-24
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although \(20x^{3}\) appears in both \(20x^{3} + 8x^{2} and 20x^{3} + 10x\), I’ll need to factor \(20x^{3}\) in different ways to obtain each polynomial’s factorization?

Answers (1)

2020-12-25
Step 1
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although \(20x^{3}\) appears in both \(20x^{3} + 8x^{2}\) and \(20x^{3} + 10x\), I’ll need to factor \(20x^{3}\) in different ways to obtain each polynomial’s factorization?
Step 2
We are given two expressions:
\(20x^{3} + 8x^{2}\)
and \(20x^{3} + 10x\)
if we factorize them,
\(20x^{3} + 8x^{2} =4x^{2}(5x+2)\)
and \(20x^{3} + 10x = 10x(2x^{2}+1)\)
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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