Answer :
To find the product of [tex]\((2x^2 + 3x - 1)\)[/tex] and [tex]\((3x + 5)\)[/tex], we need to multiply each term in the first polynomial by each term in the second polynomial. Let's do this step by step:
1. Multiply [tex]\(2x^2\)[/tex] by each term in the second polynomial:
- [tex]\(2x^2 \times 3x = 6x^3\)[/tex]
- [tex]\(2x^2 \times 5 = 10x^2\)[/tex]
2. Multiply [tex]\(3x\)[/tex] by each term in the second polynomial:
- [tex]\(3x \times 3x = 9x^2\)[/tex]
- [tex]\(3x \times 5 = 15x\)[/tex]
3. Multiply [tex]\(-1\)[/tex] by each term in the second polynomial:
- [tex]\(-1 \times 3x = -3x\)[/tex]
- [tex]\(-1 \times 5 = -5\)[/tex]
Now, combine all these results together:
[tex]\[6x^3 + 10x^2 + 9x^2 + 15x - 3x - 5\][/tex]
Next, combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(6x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(10x^2 + 9x^2 = 19x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(15x - 3x = 12x\)[/tex]
- The constant term: [tex]\(-5\)[/tex]
So, the final expression is:
[tex]\[6x^3 + 19x^2 + 12x - 5\][/tex]
Therefore, the product is answer choice A: [tex]\(6x^3 + 19x^2 + 12x - 5\)[/tex].
1. Multiply [tex]\(2x^2\)[/tex] by each term in the second polynomial:
- [tex]\(2x^2 \times 3x = 6x^3\)[/tex]
- [tex]\(2x^2 \times 5 = 10x^2\)[/tex]
2. Multiply [tex]\(3x\)[/tex] by each term in the second polynomial:
- [tex]\(3x \times 3x = 9x^2\)[/tex]
- [tex]\(3x \times 5 = 15x\)[/tex]
3. Multiply [tex]\(-1\)[/tex] by each term in the second polynomial:
- [tex]\(-1 \times 3x = -3x\)[/tex]
- [tex]\(-1 \times 5 = -5\)[/tex]
Now, combine all these results together:
[tex]\[6x^3 + 10x^2 + 9x^2 + 15x - 3x - 5\][/tex]
Next, combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(6x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(10x^2 + 9x^2 = 19x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(15x - 3x = 12x\)[/tex]
- The constant term: [tex]\(-5\)[/tex]
So, the final expression is:
[tex]\[6x^3 + 19x^2 + 12x - 5\][/tex]
Therefore, the product is answer choice A: [tex]\(6x^3 + 19x^2 + 12x - 5\)[/tex].
