Charles Kingsley

2021-12-17

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although $20{x}^{3}$ appears in both $20{x}^{3}+8{x}^{2}\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}20{x}^{3}+10x$ , I’ll need to factor $20{x}^{3}$ in different ways to obtain each polynomial’s factorization?

vicki331g8

Beginner2021-12-18Added 37 answers

Step 1

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although$20{x}^{3}$ appears in both $20{x}^{3}+8{x}^{2}\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}20{x}^{3}+10x$ , 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,

$20{x}^{3}+8{x}^{2}=4{x}^{2}(5x+2)$

and$20{x}^{3}+10x=10x(2{x}^{2}+1)$

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.

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

Step 2

We are given two expressions:

and

if we factorize them,

and

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.

ol3i4c5s4hr

Beginner2021-12-19Added 48 answers

Step 1

Given:

$20{x}^{3}+8{x}^{2}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}20{x}^{3}+10x$

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:

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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