Answer :
Let's solve the problem of multiplying the polynomials [tex]\((5x^2 + 2x + 8)(7x - 6)\)[/tex] step by step.
1. Distribute each term in the first polynomial across the second polynomial:
First, we distribute [tex]\(5x^2\)[/tex]:
[tex]\[
5x^2 \cdot 7x = 35x^3
\][/tex]
[tex]\[
5x^2 \cdot -6 = -30x^2
\][/tex]
Next, distribute [tex]\(2x\)[/tex]:
[tex]\[
2x \cdot 7x = 14x^2
\][/tex]
[tex]\[
2x \cdot -6 = -12x
\][/tex]
Finally, distribute [tex]\(8\)[/tex]:
[tex]\[
8 \cdot 7x = 56x
\][/tex]
[tex]\[
8 \cdot -6 = -48
\][/tex]
2. Combine all the terms together:
[tex]\[
35x^3 - 30x^2 + 14x^2 - 12x + 56x - 48
\][/tex]
3. Combine like terms:
- For [tex]\(x^2\)[/tex] terms: [tex]\(-30x^2 + 14x^2 = -16x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(-12x + 56x = 44x\)[/tex]
Now, combine everything:
[tex]\[
35x^3 - 16x^2 + 44x - 48
\][/tex]
The result of the multiplication is [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex].
By looking at the given answer choices, the correct one is:
B. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex]
1. Distribute each term in the first polynomial across the second polynomial:
First, we distribute [tex]\(5x^2\)[/tex]:
[tex]\[
5x^2 \cdot 7x = 35x^3
\][/tex]
[tex]\[
5x^2 \cdot -6 = -30x^2
\][/tex]
Next, distribute [tex]\(2x\)[/tex]:
[tex]\[
2x \cdot 7x = 14x^2
\][/tex]
[tex]\[
2x \cdot -6 = -12x
\][/tex]
Finally, distribute [tex]\(8\)[/tex]:
[tex]\[
8 \cdot 7x = 56x
\][/tex]
[tex]\[
8 \cdot -6 = -48
\][/tex]
2. Combine all the terms together:
[tex]\[
35x^3 - 30x^2 + 14x^2 - 12x + 56x - 48
\][/tex]
3. Combine like terms:
- For [tex]\(x^2\)[/tex] terms: [tex]\(-30x^2 + 14x^2 = -16x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(-12x + 56x = 44x\)[/tex]
Now, combine everything:
[tex]\[
35x^3 - 16x^2 + 44x - 48
\][/tex]
The result of the multiplication is [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex].
By looking at the given answer choices, the correct one is:
B. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex]
