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Answer :
Sure! Let's multiply the polynomials [tex]\((4x^2 + 3x + 7)\)[/tex] and [tex]\((8x - 5)\)[/tex] step by step.
To multiply these polynomials, we'll use the distributive property to expand the expression:
1. Multiply each term in the first polynomial by each term in the second polynomial:
- First term: [tex]\(4x^2 \times 8x = 32x^3\)[/tex]
- Second term: [tex]\(4x^2 \times (-5) = -20x^2\)[/tex]
- Third term: [tex]\(3x \times 8x = 24x^2\)[/tex]
- Fourth term: [tex]\(3x \times (-5) = -15x\)[/tex]
- Fifth term: [tex]\(7 \times 8x = 56x\)[/tex]
- Sixth term: [tex]\(7 \times (-5) = -35\)[/tex]
2. Combine like terms:
- For [tex]\(x^3\)[/tex], we have [tex]\(32x^3\)[/tex].
- For [tex]\(x^2\)[/tex], combine [tex]\(-20x^2\)[/tex] and [tex]\(24x^2\)[/tex] to get [tex]\(4x^2\)[/tex].
- For [tex]\(x\)[/tex], combine [tex]\(-15x\)[/tex] and [tex]\(56x\)[/tex] to get [tex]\(41x\)[/tex].
- The constant term is [tex]\(-35\)[/tex].
Putting it all together, the resulting polynomial is:
[tex]\[ 32x^3 + 4x^2 + 41x - 35 \][/tex]
So, the correct answer is:
C. [tex]\(32x^3 + 4x^2 + 41x - 35\)[/tex]
To multiply these polynomials, we'll use the distributive property to expand the expression:
1. Multiply each term in the first polynomial by each term in the second polynomial:
- First term: [tex]\(4x^2 \times 8x = 32x^3\)[/tex]
- Second term: [tex]\(4x^2 \times (-5) = -20x^2\)[/tex]
- Third term: [tex]\(3x \times 8x = 24x^2\)[/tex]
- Fourth term: [tex]\(3x \times (-5) = -15x\)[/tex]
- Fifth term: [tex]\(7 \times 8x = 56x\)[/tex]
- Sixth term: [tex]\(7 \times (-5) = -35\)[/tex]
2. Combine like terms:
- For [tex]\(x^3\)[/tex], we have [tex]\(32x^3\)[/tex].
- For [tex]\(x^2\)[/tex], combine [tex]\(-20x^2\)[/tex] and [tex]\(24x^2\)[/tex] to get [tex]\(4x^2\)[/tex].
- For [tex]\(x\)[/tex], combine [tex]\(-15x\)[/tex] and [tex]\(56x\)[/tex] to get [tex]\(41x\)[/tex].
- The constant term is [tex]\(-35\)[/tex].
Putting it all together, the resulting polynomial is:
[tex]\[ 32x^3 + 4x^2 + 41x - 35 \][/tex]
So, the correct answer is:
C. [tex]\(32x^3 + 4x^2 + 41x - 35\)[/tex]
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