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Multiply the polynomials.

[tex]\left(4x^2 + 3x + 7\right)(8x - 5)[/tex]

A. [tex]32x^3 - 44x^2 - 71x - 35[/tex]

B. [tex]32x^3 + 4x^2 + 41x - 35[/tex]

C. [tex]32x^3 + 4x^2 + 41x + 35[/tex]

D. [tex]32x^3 - 4x^2 - 41x + 35[/tex]

Answer :

Let's multiply the polynomials [tex]\((4x^2 + 3x + 7)\)[/tex] and [tex]\((8x - 5)\)[/tex] step-by-step.

1. Distribute each term of the first polynomial to every term of the second polynomial:

- Multiply [tex]\(4x^2\)[/tex] by each term in [tex]\(8x - 5\)[/tex]:

[tex]\[
4x^2 \times 8x = 32x^3 \\
4x^2 \times -5 = -20x^2
\][/tex]

- Multiply [tex]\(3x\)[/tex] by each term in [tex]\(8x - 5\)[/tex]:

[tex]\[
3x \times 8x = 24x^2 \\
3x \times -5 = -15x
\][/tex]

- Multiply [tex]\(7\)[/tex] by each term in [tex]\(8x - 5\)[/tex]:

[tex]\[
7 \times 8x = 56x \\
7 \times -5 = -35
\][/tex]

2. Combine all these results:

[tex]\[
32x^3 + (-20x^2 + 24x^2) + (-15x + 56x) + (-35)
\][/tex]

3. Simplify by combining like terms:

[tex]\[
32x^3 + 4x^2 + 41x - 35
\][/tex]

Now, let's compare this result with the given options:

- A. [tex]\(32x^3 - 44x^2 - 71x - 35\)[/tex]
- B. [tex]\(32x^3 + 4x^2 + 41x - 35\)[/tex]
- C. [tex]\(32x^3 + 4x^2 + 41x + 35\)[/tex]
- D. [tex]\(32x^3 - 4x^2 - 41x + 35\)[/tex]

The correct answer is B. [tex]\(32x^3 + 4x^2 + 41x - 35\)[/tex].

Thanks for taking the time to read Multiply the polynomials tex left 4x 2 3x 7 right 8x 5 tex A tex 32x 3 44x 2 71x 35 tex B tex 32x. 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!

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