Answer :
Sure, let's solve the polynomial multiplication step-by-step:
We need to multiply the two polynomials [tex]\((4x^2 + 3x + 7)(8x - 5)\)[/tex].
Here's how to do it step by step:
1. Distribute each term in the first polynomial by each term in the second polynomial:
[tex]\[
(4x^2 + 3x + 7)(8x - 5) = 4x^2 \cdot 8x + 4x^2 \cdot (-5) + 3x \cdot 8x + 3x \cdot (-5) + 7 \cdot 8x + 7 \cdot (-5)
\][/tex]
2. Multiply the terms:
[tex]\[
4x^2 \cdot 8x = 32x^3
\][/tex]
[tex]\[
4x^2 \cdot (-5) = -20x^2
\][/tex]
[tex]\[
3x \cdot 8x = 24x^2
\][/tex]
[tex]\[
3x \cdot (-5) = -15x
\][/tex]
[tex]\[
7 \cdot 8x = 56x
\][/tex]
[tex]\[
7 \cdot (-5) = -35
\][/tex]
3. Combine all the products:
[tex]\[
32x^3 - 20x^2 + 24x^2 - 15x + 56x - 35
\][/tex]
4. Combine like terms:
Combine the [tex]\(x^2\)[/tex] and [tex]\(x\)[/tex] terms:
[tex]\[
-20x^2 + 24x^2 = 4x^2
\][/tex]
[tex]\[
-15x + 56x = 41x
\][/tex]
So, the combined polynomial is:
[tex]\[
32x^3 + 4x^2 + 41x - 35
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{C. \ 32x^3 + 4x^2 + 41x - 35}
\][/tex]
We need to multiply the two polynomials [tex]\((4x^2 + 3x + 7)(8x - 5)\)[/tex].
Here's how to do it step by step:
1. Distribute each term in the first polynomial by each term in the second polynomial:
[tex]\[
(4x^2 + 3x + 7)(8x - 5) = 4x^2 \cdot 8x + 4x^2 \cdot (-5) + 3x \cdot 8x + 3x \cdot (-5) + 7 \cdot 8x + 7 \cdot (-5)
\][/tex]
2. Multiply the terms:
[tex]\[
4x^2 \cdot 8x = 32x^3
\][/tex]
[tex]\[
4x^2 \cdot (-5) = -20x^2
\][/tex]
[tex]\[
3x \cdot 8x = 24x^2
\][/tex]
[tex]\[
3x \cdot (-5) = -15x
\][/tex]
[tex]\[
7 \cdot 8x = 56x
\][/tex]
[tex]\[
7 \cdot (-5) = -35
\][/tex]
3. Combine all the products:
[tex]\[
32x^3 - 20x^2 + 24x^2 - 15x + 56x - 35
\][/tex]
4. Combine like terms:
Combine the [tex]\(x^2\)[/tex] and [tex]\(x\)[/tex] terms:
[tex]\[
-20x^2 + 24x^2 = 4x^2
\][/tex]
[tex]\[
-15x + 56x = 41x
\][/tex]
So, the combined polynomial is:
[tex]\[
32x^3 + 4x^2 + 41x - 35
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{C. \ 32x^3 + 4x^2 + 41x - 35}
\][/tex]
