Answer :
Let's multiply the polynomials [tex]\((4x^2 + 3x + 7)(8x - 5)\)[/tex] step-by-step to find the correct answer.
1. Multiply each term in the first polynomial by each term in the second polynomial:
- [tex]\(4x^2 \times 8x = 32x^3\)[/tex]
- [tex]\(4x^2 \times -5 = -20x^2\)[/tex]
- [tex]\(3x \times 8x = 24x^2\)[/tex]
- [tex]\(3x \times -5 = -15x\)[/tex]
- [tex]\(7 \times 8x = 56x\)[/tex]
- [tex]\(7 \times -5 = -35\)[/tex]
2. Combine like terms:
- For the [tex]\(x^3\)[/tex] term, we have [tex]\(32x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms, combine [tex]\(-20x^2 + 24x^2 = 4x^2\)[/tex].
- For the [tex]\(x\)[/tex] terms, combine [tex]\(-15x + 56x = 41x\)[/tex].
- The constant term is [tex]\(-35\)[/tex].
Putting it all together, the resulting polynomial is:
[tex]\[ 32x^3 + 4x^2 + 41x - 35 \][/tex]
The correct answer is:
D. [tex]\(32x^3 + 4x^2 + 41x - 35\)[/tex]
1. Multiply each term in the first polynomial by each term in the second polynomial:
- [tex]\(4x^2 \times 8x = 32x^3\)[/tex]
- [tex]\(4x^2 \times -5 = -20x^2\)[/tex]
- [tex]\(3x \times 8x = 24x^2\)[/tex]
- [tex]\(3x \times -5 = -15x\)[/tex]
- [tex]\(7 \times 8x = 56x\)[/tex]
- [tex]\(7 \times -5 = -35\)[/tex]
2. Combine like terms:
- For the [tex]\(x^3\)[/tex] term, we have [tex]\(32x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms, combine [tex]\(-20x^2 + 24x^2 = 4x^2\)[/tex].
- For the [tex]\(x\)[/tex] terms, combine [tex]\(-15x + 56x = 41x\)[/tex].
- The constant term is [tex]\(-35\)[/tex].
Putting it all together, the resulting polynomial is:
[tex]\[ 32x^3 + 4x^2 + 41x - 35 \][/tex]
The correct answer is:
D. [tex]\(32x^3 + 4x^2 + 41x - 35\)[/tex]
