Answer :
To multiply the polynomials [tex]\(x^2 + 4x + 2\)[/tex] and [tex]\(2x^2 + 3x - 4\)[/tex], we'll follow a step-by-step process:
1. Distribute Each Term:
Multiply each term in the first polynomial by each term in the second polynomial.
2. Multiplying Terms:
- Multiply [tex]\(x^2\)[/tex] by each term in the second polynomial:
- [tex]\(x^2 \times 2x^2 = 2x^4\)[/tex]
- [tex]\(x^2 \times 3x = 3x^3\)[/tex]
- [tex]\(x^2 \times (-4) = -4x^2\)[/tex]
- Multiply [tex]\(4x\)[/tex] by each term in the second polynomial:
- [tex]\(4x \times 2x^2 = 8x^3\)[/tex]
- [tex]\(4x \times 3x = 12x^2\)[/tex]
- [tex]\(4x \times (-4) = -16x\)[/tex]
- Multiply [tex]\(2\)[/tex] by each term in the second polynomial:
- [tex]\(2 \times 2x^2 = 4x^2\)[/tex]
- [tex]\(2 \times 3x = 6x\)[/tex]
- [tex]\(2 \times (-4) = -8\)[/tex]
3. Combine Like Terms:
- Collect all the terms obtained from multiplication and combine the like terms:
- [tex]\(2x^4\)[/tex]
- [tex]\(3x^3 + 8x^3 = 11x^3\)[/tex]
- [tex]\(-4x^2 + 12x^2 + 4x^2 = 12x^2\)[/tex]
- [tex]\(-16x + 6x = -10x\)[/tex]
- [tex]\(-8\)[/tex]
4. Write the Final Polynomial:
The final expression after combining like terms is:
[tex]\[2x^4 + 11x^3 + 12x^2 - 10x - 8\][/tex]
Therefore, the correct answer is:
B. [tex]\(2x^4 + 11x^3 + 12x^2 - 10x - 8\)[/tex]
1. Distribute Each Term:
Multiply each term in the first polynomial by each term in the second polynomial.
2. Multiplying Terms:
- Multiply [tex]\(x^2\)[/tex] by each term in the second polynomial:
- [tex]\(x^2 \times 2x^2 = 2x^4\)[/tex]
- [tex]\(x^2 \times 3x = 3x^3\)[/tex]
- [tex]\(x^2 \times (-4) = -4x^2\)[/tex]
- Multiply [tex]\(4x\)[/tex] by each term in the second polynomial:
- [tex]\(4x \times 2x^2 = 8x^3\)[/tex]
- [tex]\(4x \times 3x = 12x^2\)[/tex]
- [tex]\(4x \times (-4) = -16x\)[/tex]
- Multiply [tex]\(2\)[/tex] by each term in the second polynomial:
- [tex]\(2 \times 2x^2 = 4x^2\)[/tex]
- [tex]\(2 \times 3x = 6x\)[/tex]
- [tex]\(2 \times (-4) = -8\)[/tex]
3. Combine Like Terms:
- Collect all the terms obtained from multiplication and combine the like terms:
- [tex]\(2x^4\)[/tex]
- [tex]\(3x^3 + 8x^3 = 11x^3\)[/tex]
- [tex]\(-4x^2 + 12x^2 + 4x^2 = 12x^2\)[/tex]
- [tex]\(-16x + 6x = -10x\)[/tex]
- [tex]\(-8\)[/tex]
4. Write the Final Polynomial:
The final expression after combining like terms is:
[tex]\[2x^4 + 11x^3 + 12x^2 - 10x - 8\][/tex]
Therefore, the correct answer is:
B. [tex]\(2x^4 + 11x^3 + 12x^2 - 10x - 8\)[/tex]
