Answer :
Sure, I'll show you how to multiply these two polynomials step-by-step.
We need to multiply [tex]\((3x^2 - 7x + 4)\)[/tex] by [tex]\((5x^2 + 2x)\)[/tex].
First, let's distribute each term in the first polynomial [tex]\((3x^2 - 7x + 4)\)[/tex] across each term in the second polynomial [tex]\((5x^2 + 2x)\)[/tex]:
[tex]\[
(3x^2 - 7x + 4) \times (5x^2 + 2x)
\][/tex]
Distribute [tex]\(3x^2\)[/tex]:
[tex]\[
3x^2 \cdot 5x^2 + 3x^2 \cdot 2x = 15x^4 + 6x^3
\][/tex]
Distribute [tex]\(-7x\)[/tex]:
[tex]\[
-7x \cdot 5x^2 + -7x \cdot 2x = -35x^3 - 14x^2
\][/tex]
Distribute [tex]\(4\)[/tex]:
[tex]\[
4 \cdot 5x^2 + 4 \cdot 2x = 20x^2 + 8x
\][/tex]
Now, combine all the terms we calculated:
[tex]\[
15x^4 + 6x^3 - 35x^3 - 14x^2 + 20x^2 + 8x
\][/tex]
Combine like terms:
[tex]\[
15x^4 + (6x^3 - 35x^3) + (-14x^2 + 20x^2) + 8x
\][/tex]
Simplify the coefficients:
[tex]\[
15x^4 - 29x^3 + 6x^2 + 8x
\][/tex]
So the solution is:
D. [tex]\(15x^4 - 29x^3 + 20x^2 + 8x\)[/tex]
We need to multiply [tex]\((3x^2 - 7x + 4)\)[/tex] by [tex]\((5x^2 + 2x)\)[/tex].
First, let's distribute each term in the first polynomial [tex]\((3x^2 - 7x + 4)\)[/tex] across each term in the second polynomial [tex]\((5x^2 + 2x)\)[/tex]:
[tex]\[
(3x^2 - 7x + 4) \times (5x^2 + 2x)
\][/tex]
Distribute [tex]\(3x^2\)[/tex]:
[tex]\[
3x^2 \cdot 5x^2 + 3x^2 \cdot 2x = 15x^4 + 6x^3
\][/tex]
Distribute [tex]\(-7x\)[/tex]:
[tex]\[
-7x \cdot 5x^2 + -7x \cdot 2x = -35x^3 - 14x^2
\][/tex]
Distribute [tex]\(4\)[/tex]:
[tex]\[
4 \cdot 5x^2 + 4 \cdot 2x = 20x^2 + 8x
\][/tex]
Now, combine all the terms we calculated:
[tex]\[
15x^4 + 6x^3 - 35x^3 - 14x^2 + 20x^2 + 8x
\][/tex]
Combine like terms:
[tex]\[
15x^4 + (6x^3 - 35x^3) + (-14x^2 + 20x^2) + 8x
\][/tex]
Simplify the coefficients:
[tex]\[
15x^4 - 29x^3 + 6x^2 + 8x
\][/tex]
So the solution is:
D. [tex]\(15x^4 - 29x^3 + 20x^2 + 8x\)[/tex]
