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Multiply the polynomials:

[tex]\left(7x^2 + 5x + 7\right)(4x - 6)[/tex]

A. [tex]28x^3 - 22x^2 - 2x + 42[/tex]

B. [tex]28x^3 - 22x^2 - 58x - 42[/tex]

C. [tex]28x^3 - 62x^2 - 2x - 42[/tex]

D. [tex]28x^3 - 22x^2 - 2x - 42[/tex]

Answer :

Sure, let's multiply the polynomials step-by-step. We want to find the product of [tex]\((7x^2 + 5x + 7)(4x - 6)\)[/tex].

1. Distribute [tex]\(7x^2\)[/tex]:

[tex]\[
7x^2 \cdot (4x) = 28x^3
\][/tex]
[tex]\[
7x^2 \cdot (-6) = -42x^2
\][/tex]

2. Distribute [tex]\(5x\)[/tex]:

[tex]\[
5x \cdot (4x) = 20x^2
\][/tex]
[tex]\[
5x \cdot (-6) = -30x
\][/tex]

3. Distribute [tex]\(7\)[/tex]:

[tex]\[
7 \cdot (4x) = 28x
\][/tex]
[tex]\[
7 \cdot (-6) = -42
\][/tex]

4. Combine like terms:

- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-42x^2 + 20x^2 = -22x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-30x + 28x = -2x\)[/tex]

5. Write the final expression:

So, the result of the multiplication is:

[tex]\[
28x^3 - 22x^2 - 2x - 42
\][/tex]

Thus, the correct answer is D. [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex].

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