Answer :
Sure! Let's multiply the polynomials step by step:
We need to multiply [tex]\((5x^2 + 2x + 8)\)[/tex] by [tex]\((7x - 6)\)[/tex].
To do this, we'll use the distributive property, which means we'll multiply each term in the first polynomial by each term in the second polynomial.
Step 1: Multiply [tex]\(5x^2\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(5x^2 \times 7x = 35x^3\)[/tex]
- [tex]\(5x^2 \times (-6) = -30x^2\)[/tex]
Step 2: Multiply [tex]\(2x\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(2x \times 7x = 14x^2\)[/tex]
- [tex]\(2x \times (-6) = -12x\)[/tex]
Step 3: Multiply [tex]\(8\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(8 \times 7x = 56x\)[/tex]
- [tex]\(8 \times (-6) = -48\)[/tex]
Now, let's add up all these results:
- For [tex]\(x^3\)[/tex] term: [tex]\(35x^3\)[/tex]
- For [tex]\(x^2\)[/tex] terms: [tex]\(-30x^2 + 14x^2 = -16x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(-12x + 56x = 44x\)[/tex]
- Constant term: [tex]\(-48\)[/tex]
So the result of multiplying the polynomials is:
[tex]\[ 35x^3 - 16x^2 + 44x - 48 \][/tex]
Thus, the correct answer is:
Option D. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex]
We need to multiply [tex]\((5x^2 + 2x + 8)\)[/tex] by [tex]\((7x - 6)\)[/tex].
To do this, we'll use the distributive property, which means we'll multiply each term in the first polynomial by each term in the second polynomial.
Step 1: Multiply [tex]\(5x^2\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(5x^2 \times 7x = 35x^3\)[/tex]
- [tex]\(5x^2 \times (-6) = -30x^2\)[/tex]
Step 2: Multiply [tex]\(2x\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(2x \times 7x = 14x^2\)[/tex]
- [tex]\(2x \times (-6) = -12x\)[/tex]
Step 3: Multiply [tex]\(8\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(8 \times 7x = 56x\)[/tex]
- [tex]\(8 \times (-6) = -48\)[/tex]
Now, let's add up all these results:
- For [tex]\(x^3\)[/tex] term: [tex]\(35x^3\)[/tex]
- For [tex]\(x^2\)[/tex] terms: [tex]\(-30x^2 + 14x^2 = -16x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(-12x + 56x = 44x\)[/tex]
- Constant term: [tex]\(-48\)[/tex]
So the result of multiplying the polynomials is:
[tex]\[ 35x^3 - 16x^2 + 44x - 48 \][/tex]
Thus, the correct answer is:
Option D. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex]
