We appreciate your visit to Factor the four term polynomial by grouping tex 12x 3 20x 2 15x 25 tex Select the correct choice below A tex 12x 3 20x. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We start with the polynomial
[tex]$$
12x^3 - 20x^2 + 15x - 25.
$$[/tex]
Step 1. Group Terms
Group the polynomial into two groups:
[tex]$$
(12x^3 - 20x^2) + (15x - 25).
$$[/tex]
Step 2. Factor Common Factors in Each Group
In the first group, factor out the greatest common factor (GCF) [tex]$4x^2$[/tex]:
[tex]$$
12x^3 - 20x^2 = 4x^2(3x - 5).
$$[/tex]
In the second group, factor out the GCF [tex]$5$[/tex]:
[tex]$$
15x - 25 = 5(3x - 5).
$$[/tex]
Step 3. Factor Out the Common Binomial
Notice that both groups now contain the common factor [tex]$(3x-5)$[/tex]. Factor this binomial out:
[tex]$$
4x^2(3x-5) + 5(3x-5) = (3x-5)\left(4x^2 + 5\right).
$$[/tex]
Final Answer
Thus, the factored form of the polynomial is:
[tex]$$
12x^3 - 20x^2 + 15x - 25 = (3x-5)(4x^2+5).
$$[/tex]
Select choice A with the filled box:
[tex]$$
\boxed{(3x-5)(4x^2+5)}
$$[/tex]
[tex]$$
12x^3 - 20x^2 + 15x - 25.
$$[/tex]
Step 1. Group Terms
Group the polynomial into two groups:
[tex]$$
(12x^3 - 20x^2) + (15x - 25).
$$[/tex]
Step 2. Factor Common Factors in Each Group
In the first group, factor out the greatest common factor (GCF) [tex]$4x^2$[/tex]:
[tex]$$
12x^3 - 20x^2 = 4x^2(3x - 5).
$$[/tex]
In the second group, factor out the GCF [tex]$5$[/tex]:
[tex]$$
15x - 25 = 5(3x - 5).
$$[/tex]
Step 3. Factor Out the Common Binomial
Notice that both groups now contain the common factor [tex]$(3x-5)$[/tex]. Factor this binomial out:
[tex]$$
4x^2(3x-5) + 5(3x-5) = (3x-5)\left(4x^2 + 5\right).
$$[/tex]
Final Answer
Thus, the factored form of the polynomial is:
[tex]$$
12x^3 - 20x^2 + 15x - 25 = (3x-5)(4x^2+5).
$$[/tex]
Select choice A with the filled box:
[tex]$$
\boxed{(3x-5)(4x^2+5)}
$$[/tex]
Thanks for taking the time to read Factor the four term polynomial by grouping tex 12x 3 20x 2 15x 25 tex Select the correct choice below A tex 12x 3 20x. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
