Answered

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The polynomial [tex]$10x^3 + 35x^2 - 4x - 14$[/tex] is factored by grouping.

[tex]\[
\begin{array}{l}
10x^3 + 35x^2 - 4x - 14 \\
5x^2(\square) - 2(\square)
\end{array}
\][/tex]

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

A. [tex]-2x - 7[/tex]
B. [tex]2x + 7[/tex]
C. [tex]-2x^2 + 7[/tex]
D. [tex]2x^2 + 7[/tex]

Sagot :

GinnyAnswer
To factor the polynomial [tex]\(10x^3 + 35x^2 - 4x - 14\)[/tex] by grouping, follow these steps:

1. Group the terms:
Separate the polynomial into two groups:
[tex]\[ (10x^3 + 35x^2) + (-4x - 14) \][/tex]

2. Factor out the Greatest Common Factor (GCF) from each group:
- For the first group [tex]\((10x^3 + 35x^2)\)[/tex], the GCF is [tex]\(5x^2\)[/tex]:
[tex]\[ 10x^3 + 35x^2 = 5x^2(2x + 7) \][/tex]
- For the second group [tex]\((-4x - 14)\)[/tex], the GCF is [tex]\(-2\)[/tex]:
[tex]\[ -4x - 14 = -2(2x + 7) \][/tex]

3. Rewrite the polynomial with the factored terms:
[tex]\[ 10x^3 + 35x^2 - 4x - 14 = 5x^2(2x + 7) - 2(2x + 7) \][/tex]

4. Identify the common factor in both terms:
Both terms contain the common binomial factor [tex]\((2x + 7)\)[/tex].

Therefore, the correct missing factor in both sets of parentheses is:

[tex]\[ \boxed{2x + 7} \][/tex]
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