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Answer :
To find the product of two polynomials, you multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
Let's find the product of [tex]\((2x^2 + 3x - 1)\)[/tex] and [tex]\((3x + 5)\)[/tex]:
### Step 1: Distribute each term in the first polynomial:
- Multiply [tex]\(2x^2\)[/tex] by each term in the second polynomial [tex]\((3x + 5)\)[/tex]:
- [tex]\(2x^2 \cdot 3x = 6x^3\)[/tex]
- [tex]\(2x^2 \cdot 5 = 10x^2\)[/tex]
- Multiply [tex]\(3x\)[/tex] by each term in the second polynomial [tex]\((3x + 5)\)[/tex]:
- [tex]\(3x \cdot 3x = 9x^2\)[/tex]
- [tex]\(3x \cdot 5 = 15x\)[/tex]
- Multiply [tex]\(-1\)[/tex] by each term in the second polynomial [tex]\((3x + 5)\)[/tex]:
- [tex]\(-1 \cdot 3x = -3x\)[/tex]
- [tex]\(-1 \cdot 5 = -5\)[/tex]
### Step 2: Combine all the terms:
Putting all the terms together, we get:
[tex]\[6x^3 + 10x^2 + 9x^2 + 15x - 3x - 5\][/tex]
### Step 3: Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(10x^2 + 9x^2 = 19x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(15x - 3x = 12x\)[/tex]
### Final Result:
The product of the polynomials is:
[tex]\[6x^3 + 19x^2 + 12x - 5\][/tex]
So, the correct answer is B. [tex]\(6x^3 + 19x^2 + 12x - 5\)[/tex].
Let's find the product of [tex]\((2x^2 + 3x - 1)\)[/tex] and [tex]\((3x + 5)\)[/tex]:
### Step 1: Distribute each term in the first polynomial:
- Multiply [tex]\(2x^2\)[/tex] by each term in the second polynomial [tex]\((3x + 5)\)[/tex]:
- [tex]\(2x^2 \cdot 3x = 6x^3\)[/tex]
- [tex]\(2x^2 \cdot 5 = 10x^2\)[/tex]
- Multiply [tex]\(3x\)[/tex] by each term in the second polynomial [tex]\((3x + 5)\)[/tex]:
- [tex]\(3x \cdot 3x = 9x^2\)[/tex]
- [tex]\(3x \cdot 5 = 15x\)[/tex]
- Multiply [tex]\(-1\)[/tex] by each term in the second polynomial [tex]\((3x + 5)\)[/tex]:
- [tex]\(-1 \cdot 3x = -3x\)[/tex]
- [tex]\(-1 \cdot 5 = -5\)[/tex]
### Step 2: Combine all the terms:
Putting all the terms together, we get:
[tex]\[6x^3 + 10x^2 + 9x^2 + 15x - 3x - 5\][/tex]
### Step 3: Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(10x^2 + 9x^2 = 19x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(15x - 3x = 12x\)[/tex]
### Final Result:
The product of the polynomials is:
[tex]\[6x^3 + 19x^2 + 12x - 5\][/tex]
So, the correct answer is B. [tex]\(6x^3 + 19x^2 + 12x - 5\)[/tex].
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