Answer :
Let's multiply the polynomials [tex]\((5x^2 + 2x + 8)(7x - 6)\)[/tex].
We will distribute each term in the first polynomial by each term in the second polynomial and then simplify:
1. Multiply the first term of the first polynomial by both terms of the second polynomial:
- [tex]\(5x^2 \times 7x = 35x^3\)[/tex]
- [tex]\(5x^2 \times -6 = -30x^2\)[/tex]
2. Multiply the second term of the first polynomial by both terms of the second polynomial:
- [tex]\(2x \times 7x = 14x^2\)[/tex]
- [tex]\(2x \times -6 = -12x\)[/tex]
3. Multiply the third term of the first polynomial by both terms of the second polynomial:
- [tex]\(8 \times 7x = 56x\)[/tex]
- [tex]\(8 \times -6 = -48\)[/tex]
Now, add up all these results, combining like terms:
- The [tex]\(x^3\)[/tex] term is: [tex]\(35x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-30x^2 + 14x^2 = -16x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-12x + 56x = 44x\)[/tex]
- The constant term is: [tex]\(-48\)[/tex]
Putting it all together, the result of multiplying the polynomials is:
[tex]\[35x^3 - 16x^2 + 44x - 48\][/tex]
Therefore, the correct answer is:
C. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex]
We will distribute each term in the first polynomial by each term in the second polynomial and then simplify:
1. Multiply the first term of the first polynomial by both terms of the second polynomial:
- [tex]\(5x^2 \times 7x = 35x^3\)[/tex]
- [tex]\(5x^2 \times -6 = -30x^2\)[/tex]
2. Multiply the second term of the first polynomial by both terms of the second polynomial:
- [tex]\(2x \times 7x = 14x^2\)[/tex]
- [tex]\(2x \times -6 = -12x\)[/tex]
3. Multiply the third term of the first polynomial by both terms of the second polynomial:
- [tex]\(8 \times 7x = 56x\)[/tex]
- [tex]\(8 \times -6 = -48\)[/tex]
Now, add up all these results, combining like terms:
- The [tex]\(x^3\)[/tex] term is: [tex]\(35x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-30x^2 + 14x^2 = -16x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-12x + 56x = 44x\)[/tex]
- The constant term is: [tex]\(-48\)[/tex]
Putting it all together, the result of multiplying the polynomials is:
[tex]\[35x^3 - 16x^2 + 44x - 48\][/tex]
Therefore, the correct answer is:
C. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex]
