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?

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?

Question
Polynomial factorization
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.
0

Relevant Questions

asked 2020-11-01
The term \(20x^{3}\) appears in both the expressions \(20x^{3} + 8x^{2}\) and \(20x^{3} + 10x\) but factor \(20x^{3}\) in different ways to obtain each polynomial factorization Whether the given statement make sense or does not make sence.
asked 2021-01-15
Determine whether the statement, "The word identity is used in different ways in additive identity, multiplicative identity, and trigonometric identity". makes sense or does not make sense, and explain your reasoning.
asked 2021-05-14
Use two different groupings to factor ac-ad+bd-bc in two ways. Then explain why the two factorizations are the same.
asked 2020-10-21
Determine whether the statement, 'I noticed that depending on the values for A and C, assuming that they are not both zero, the graph of \(\displaystyle{A}{x}^{{{2}}}+{C}{y}^{{{2}}}+{D}{x}+{E}{y}+{F}={0}\) can represent any of the conic sections', makes sense or does not make sense, and explain your reasoning.
asked 2021-02-25
Each equation in a system of linear equations has infinitely many ordered-pair solutions.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
asked 2020-11-05
Determine whether each statement makes sense or does not make sense, and explain your reasoning. A system of linear equations in three variables, x, y, and z, cannot contain an equation in the form y = mx + b.
asked 2021-02-13
Whether the statement “I noticed that depending on the values for Aand B assuming that they are not both zero, the graph of \(Ax^2 + By^2 = C\) can represent any of the conic sections other than a parabola” “makes sense” or “does not make sense”, And explain your reasoning.
asked 2021-05-30
Use the factorization theorem to determine whether \(x-\frac{1}{2}\) is a factor of \(f(x) = 2x^{4}-x^{3}=2x-1\).
asked 2021-02-24
I’m solving a three-variable system in which one of the given equations has a missing term, so it will not be necessary to use any of the original equations twice when I reduce the system to two equations in two variables.Determine whether the statement makes sense or does not make sense, and explain your reasoning
asked 2021-03-12
When using the half-angle formulas for trigonometric functions of \(alpha/2\), I determine the sign based on the quadrant in which \(alpha\) lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
...