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Answer :
Sure! Let's multiply the two polynomials step by step:
We are given:
[tex]\[ (x^2 + 4x + 2) \times (2x^2 + 3x - 4) \][/tex]
We can multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
### Step-by-step calculation:
1. Multiply each term in [tex]\(x^2 + 4x + 2\)[/tex] by [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 [tex]\(x^2 + 4x + 2\)[/tex] by [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 [tex]\(x^2 + 4x + 2\)[/tex] by [tex]\(-4\)[/tex]:
- [tex]\(x^2 \times -4 = -4x^2\)[/tex]
- [tex]\(4x \times -4 = -16x\)[/tex]
- [tex]\(2 \times -4 = -8\)[/tex]
### Adding all these results together:
- [tex]\(2x^4\)[/tex]
- [tex]\(8x^3 + 3x^3 = 11x^3\)[/tex]
- [tex]\(4x^2 + 12x^2 - 4x^2 = 12x^2\)[/tex]
- [tex]\(6x - 16x = -10x\)[/tex]
- [tex]\(-8\)[/tex]
Therefore, the expanded form of the polynomial is:
[tex]\[ 2x^4 + 11x^3 + 12x^2 - 10x - 8 \][/tex]
The correct answer is C. [tex]\(2x^4 + 11x^3 + 12x^2 - 10x - 8\)[/tex].
We are given:
[tex]\[ (x^2 + 4x + 2) \times (2x^2 + 3x - 4) \][/tex]
We can multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
### Step-by-step calculation:
1. Multiply each term in [tex]\(x^2 + 4x + 2\)[/tex] by [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 [tex]\(x^2 + 4x + 2\)[/tex] by [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 [tex]\(x^2 + 4x + 2\)[/tex] by [tex]\(-4\)[/tex]:
- [tex]\(x^2 \times -4 = -4x^2\)[/tex]
- [tex]\(4x \times -4 = -16x\)[/tex]
- [tex]\(2 \times -4 = -8\)[/tex]
### Adding all these results together:
- [tex]\(2x^4\)[/tex]
- [tex]\(8x^3 + 3x^3 = 11x^3\)[/tex]
- [tex]\(4x^2 + 12x^2 - 4x^2 = 12x^2\)[/tex]
- [tex]\(6x - 16x = -10x\)[/tex]
- [tex]\(-8\)[/tex]
Therefore, the expanded form of the polynomial is:
[tex]\[ 2x^4 + 11x^3 + 12x^2 - 10x - 8 \][/tex]
The correct answer is C. [tex]\(2x^4 + 11x^3 + 12x^2 - 10x - 8\)[/tex].
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Rewritten by : Barada
