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Answer :
To multiply the polynomials [tex]\((5x^2 + 2x + 8)\)[/tex] and [tex]\((7x - 6)\)[/tex], we'll distribute each term in the first polynomial by each term in the second polynomial. Here's a step-by-step breakdown:
1. Distribute [tex]\(7x\)[/tex] from [tex]\((7x - 6)\)[/tex] to each term in [tex]\((5x^2 + 2x + 8)\)[/tex]:
- [tex]\(7x \times 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \times 2x = 14x^2\)[/tex]
- [tex]\(7x \times 8 = 56x\)[/tex]
2. Distribute [tex]\(-6\)[/tex] from [tex]\((7x - 6)\)[/tex] to each term in [tex]\((5x^2 + 2x + 8)\)[/tex]:
- [tex]\(-6 \times 5x^2 = -30x^2\)[/tex]
- [tex]\(-6 \times 2x = -12x\)[/tex]
- [tex]\(-6 \times 8 = -48\)[/tex]
3. Combine like terms from the distributed products:
- Combine [tex]\(x^3\)[/tex] terms: [tex]\(35x^3\)[/tex]
- Combine [tex]\(x^2\)[/tex] terms: [tex]\(14x^2 - 30x^2 = -16x^2\)[/tex]
- Combine [tex]\(x\)[/tex] terms: [tex]\(56x - 12x = 44x\)[/tex]
- The constant term is [tex]\(-48\)[/tex]
Therefore, the product of [tex]\((5x^2 + 2x + 8)\)[/tex] and [tex]\((7x - 6)\)[/tex] is:
[tex]\[ 35x^3 - 16x^2 + 44x - 48 \][/tex]
So, the correct answer is A. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex].
1. Distribute [tex]\(7x\)[/tex] from [tex]\((7x - 6)\)[/tex] to each term in [tex]\((5x^2 + 2x + 8)\)[/tex]:
- [tex]\(7x \times 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \times 2x = 14x^2\)[/tex]
- [tex]\(7x \times 8 = 56x\)[/tex]
2. Distribute [tex]\(-6\)[/tex] from [tex]\((7x - 6)\)[/tex] to each term in [tex]\((5x^2 + 2x + 8)\)[/tex]:
- [tex]\(-6 \times 5x^2 = -30x^2\)[/tex]
- [tex]\(-6 \times 2x = -12x\)[/tex]
- [tex]\(-6 \times 8 = -48\)[/tex]
3. Combine like terms from the distributed products:
- Combine [tex]\(x^3\)[/tex] terms: [tex]\(35x^3\)[/tex]
- Combine [tex]\(x^2\)[/tex] terms: [tex]\(14x^2 - 30x^2 = -16x^2\)[/tex]
- Combine [tex]\(x\)[/tex] terms: [tex]\(56x - 12x = 44x\)[/tex]
- The constant term is [tex]\(-48\)[/tex]
Therefore, the product of [tex]\((5x^2 + 2x + 8)\)[/tex] and [tex]\((7x - 6)\)[/tex] is:
[tex]\[ 35x^3 - 16x^2 + 44x - 48 \][/tex]
So, the correct answer is A. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex].
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