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Answer :
To multiply the polynomials [tex]\((4x^2 + 3x + 7)(8x - 5)\)[/tex], we will distribute each term from the first polynomial to each term of the second polynomial and then combine like terms. Let's go through this step-by-step:
1. Distribute [tex]\(4x^2\)[/tex] to each term in the second polynomial:
- [tex]\(4x^2 \cdot 8x = 32x^3\)[/tex]
- [tex]\(4x^2 \cdot (-5) = -20x^2\)[/tex]
2. Distribute [tex]\(3x\)[/tex] to each term in the second polynomial:
- [tex]\(3x \cdot 8x = 24x^2\)[/tex]
- [tex]\(3x \cdot (-5) = -15x\)[/tex]
3. Distribute [tex]\(7\)[/tex] to each term in the second polynomial:
- [tex]\(7 \cdot 8x = 56x\)[/tex]
- [tex]\(7 \cdot (-5) = -35\)[/tex]
Now, let's combine all these results:
- The [tex]\(x^3\)[/tex] term is [tex]\(32x^3\)[/tex].
- The [tex]\(x^2\)[/tex] terms are [tex]\(-20x^2 + 24x^2 = 4x^2\)[/tex].
- The [tex]\(x\)[/tex] terms are [tex]\(-15x + 56x = 41x\)[/tex].
- The constant term is [tex]\(-35\)[/tex].
Combining these, we get the final result:
[tex]\[
32x^3 + 4x^2 + 41x - 35
\][/tex]
Thus, the correct choice is A. [tex]\(32x^3 + 4x^2 + 41x - 35\)[/tex].
1. Distribute [tex]\(4x^2\)[/tex] to each term in the second polynomial:
- [tex]\(4x^2 \cdot 8x = 32x^3\)[/tex]
- [tex]\(4x^2 \cdot (-5) = -20x^2\)[/tex]
2. Distribute [tex]\(3x\)[/tex] to each term in the second polynomial:
- [tex]\(3x \cdot 8x = 24x^2\)[/tex]
- [tex]\(3x \cdot (-5) = -15x\)[/tex]
3. Distribute [tex]\(7\)[/tex] to each term in the second polynomial:
- [tex]\(7 \cdot 8x = 56x\)[/tex]
- [tex]\(7 \cdot (-5) = -35\)[/tex]
Now, let's combine all these results:
- The [tex]\(x^3\)[/tex] term is [tex]\(32x^3\)[/tex].
- The [tex]\(x^2\)[/tex] terms are [tex]\(-20x^2 + 24x^2 = 4x^2\)[/tex].
- The [tex]\(x\)[/tex] terms are [tex]\(-15x + 56x = 41x\)[/tex].
- The constant term is [tex]\(-35\)[/tex].
Combining these, we get the final result:
[tex]\[
32x^3 + 4x^2 + 41x - 35
\][/tex]
Thus, the correct choice is A. [tex]\(32x^3 + 4x^2 + 41x - 35\)[/tex].
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