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Answer :
To multiply two polynomials, you need to distribute each term in the first polynomial by each term in the second polynomial. Let's break this down step-by-step using the given polynomials:
Given polynomials:
1. [tex]\( x^2 + 4x + 2 \)[/tex]
2. [tex]\( 2x^2 + 3x - 4 \)[/tex]
Follow the distributive property to multiply each term:
1. Multiply each term in the first polynomial by the first term of the second polynomial ([tex]\(2x^2\)[/tex]):
- [tex]\(x^2 \times 2x^2 = 2x^4\)[/tex]
- [tex]\(4x \times 2x^2 = 8x^3\)[/tex]
- [tex]\(2 \times 2x^2 = 4x^2\)[/tex]
2. Multiply each term in the first polynomial by the second term of the second polynomial ([tex]\(3x\)[/tex]):
- [tex]\(x^2 \times 3x = 3x^3\)[/tex]
- [tex]\(4x \times 3x = 12x^2\)[/tex]
- [tex]\(2 \times 3x = 6x\)[/tex]
3. Multiply each term in the first polynomial by the third term of the second polynomial ([tex]\(-4\)[/tex]):
- [tex]\(x^2 \times -4 = -4x^2\)[/tex]
- [tex]\(4x \times -4 = -16x\)[/tex]
- [tex]\(2 \times -4 = -8\)[/tex]
Next, combine all the products by adding like terms:
- [tex]\(2x^4\)[/tex] (only one [tex]\(x^4\)[/tex] term)
- Combine [tex]\(8x^3 + 3x^3 = 11x^3\)[/tex]
- Combine [tex]\(4x^2 + 12x^2 - 4x^2 = 12x^2\)[/tex]
- Combine [tex]\(6x - 16x = -10x\)[/tex]
- [tex]\(-8\)[/tex] (constant term)
Putting it all together, the result of the multiplication is:
[tex]\[ 2x^4 + 11x^3 + 12x^2 - 10x - 8 \][/tex]
So, the correct answer is:
B. [tex]\(2x^4 + 11x^3 + 12x^2 - 10x - 8\)[/tex]
Given polynomials:
1. [tex]\( x^2 + 4x + 2 \)[/tex]
2. [tex]\( 2x^2 + 3x - 4 \)[/tex]
Follow the distributive property to multiply each term:
1. Multiply each term in the first polynomial by the first term of the second polynomial ([tex]\(2x^2\)[/tex]):
- [tex]\(x^2 \times 2x^2 = 2x^4\)[/tex]
- [tex]\(4x \times 2x^2 = 8x^3\)[/tex]
- [tex]\(2 \times 2x^2 = 4x^2\)[/tex]
2. Multiply each term in the first polynomial by the second term of the second polynomial ([tex]\(3x\)[/tex]):
- [tex]\(x^2 \times 3x = 3x^3\)[/tex]
- [tex]\(4x \times 3x = 12x^2\)[/tex]
- [tex]\(2 \times 3x = 6x\)[/tex]
3. Multiply each term in the first polynomial by the third term of the second polynomial ([tex]\(-4\)[/tex]):
- [tex]\(x^2 \times -4 = -4x^2\)[/tex]
- [tex]\(4x \times -4 = -16x\)[/tex]
- [tex]\(2 \times -4 = -8\)[/tex]
Next, combine all the products by adding like terms:
- [tex]\(2x^4\)[/tex] (only one [tex]\(x^4\)[/tex] term)
- Combine [tex]\(8x^3 + 3x^3 = 11x^3\)[/tex]
- Combine [tex]\(4x^2 + 12x^2 - 4x^2 = 12x^2\)[/tex]
- Combine [tex]\(6x - 16x = -10x\)[/tex]
- [tex]\(-8\)[/tex] (constant term)
Putting it all together, the result of the multiplication is:
[tex]\[ 2x^4 + 11x^3 + 12x^2 - 10x - 8 \][/tex]
So, the correct answer is:
B. [tex]\(2x^4 + 11x^3 + 12x^2 - 10x - 8\)[/tex]
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