Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

The polynomial [tex]$24 x^3-54 x^2+44 x-99$[/tex] is factored by grouping.

[tex]\[
\begin{array}{l}
24 x^3-54 x^2+44 x-99 \\
24 x^3+44 x-54 x^2-99 \\
4 x(\ldots)-9(\ldots \ldots)
\end{array}
\][/tex]

What is the common factor that is missing from both sets of parentheses?

A. [tex]6 x + 11[/tex]
B. [tex]6 x - 11[/tex]
C. [tex]6 x^2 + 11[/tex]
D. [tex]6 x^2 - 11[/tex]

Sagot :

GinnyAnswer
To factor the polynomial [tex]\(24x^3 - 54x^2 + 44x - 99\)[/tex] by grouping, let's break down the steps:

1. Group the terms appropriately:
[tex]\[ 24x^3 - 54x^2 + 44x - 99 \][/tex]
Group as:
[tex]\[ (24x^3 - 54x^2) + (44x - 99) \][/tex]

2. Factor out the greatest common factor (GCF) from each group:
- For the first group [tex]\(24x^3 - 54x^2\)[/tex], the GCF is [tex]\(6x^2\)[/tex]:
[tex]\[ 24x^3 - 54x^2 = 6x^2(4x - 9) \][/tex]
- For the second group [tex]\(44x - 99\)[/tex], the GCF is [tex]\(11\)[/tex]:
[tex]\[ 44x - 99 = 11(4x - 9) \][/tex]

3. Notice that after factoring out the GCF from each group, the binomial factors [tex]\(4x - 9\)[/tex] are common:
[tex]\[ 24x^3 - 54x^2 + 44x - 99 = 6x^2(4x - 9) + 11(4x - 9) \][/tex]

4. Factor out the common binomial factor [tex]\((4x - 9)\)[/tex]:
[tex]\[ 6x^2(4x - 9) + 11(4x - 9) = (4x - 9)(6x^2 + 11) \][/tex]

Therefore, the common factor that is missing from both sets of parentheses is:
[tex]\[ 6x^2 + 11 \][/tex]

So, the correct answer is:
```
6 x^2 + 11
```
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.