Answer :
Sure! Let's find the product of the given factors step-by-step:
The factors are [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex].
### Step-by-Step Solution
1. Distribute each term in the first factor by each term in the second factor:
[tex]\[
(2x + 5)(7 - 4x)
\][/tex]
2. Use the distributive property (also known as the FOIL method for binomials):
- First: [tex]\(2x \cdot 7 = 14x\)[/tex]
- Outer: [tex]\(2x \cdot (-4x) = -8x^2\)[/tex]
- Inner: [tex]\(5 \cdot 7 = 35\)[/tex]
- Last: [tex]\(5 \cdot (-4x) = -20x\)[/tex]
3. Combine all the products:
[tex]\[
14x + (-8x^2) + 35 + (-20x)
\][/tex]
4. Combine like terms:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
Simplify the [tex]\(x\)[/tex]-terms:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
### Conclusion
The quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
So, the correct answer is:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
The factors are [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex].
### Step-by-Step Solution
1. Distribute each term in the first factor by each term in the second factor:
[tex]\[
(2x + 5)(7 - 4x)
\][/tex]
2. Use the distributive property (also known as the FOIL method for binomials):
- First: [tex]\(2x \cdot 7 = 14x\)[/tex]
- Outer: [tex]\(2x \cdot (-4x) = -8x^2\)[/tex]
- Inner: [tex]\(5 \cdot 7 = 35\)[/tex]
- Last: [tex]\(5 \cdot (-4x) = -20x\)[/tex]
3. Combine all the products:
[tex]\[
14x + (-8x^2) + 35 + (-20x)
\][/tex]
4. Combine like terms:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
Simplify the [tex]\(x\)[/tex]-terms:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
### Conclusion
The quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
So, the correct answer is:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
