Answer :
Sure! Let's multiply the polynomials step-by-step:
We want to multiply [tex]\((x^2 - 5x)\)[/tex] by [tex]\((2x^2 + x - 3)\)[/tex]. We will use distribution to expand the expression:
1. Distribute [tex]\(x^2\)[/tex]:
- [tex]\(x^2 \cdot 2x^2 = 2x^4\)[/tex]
- [tex]\(x^2 \cdot x = x^3\)[/tex]
- [tex]\(x^2 \cdot (-3) = -3x^2\)[/tex]
2. Distribute [tex]\(-5x\)[/tex]:
- [tex]\(-5x \cdot 2x^2 = -10x^3\)[/tex]
- [tex]\(-5x \cdot x = -5x^2\)[/tex]
- [tex]\(-5x \cdot (-3) = 15x\)[/tex]
Now, combine all these terms:
- [tex]\(2x^4\)[/tex]
- [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- [tex]\(15x\)[/tex]
So, the product is:
[tex]\[ 2x^4 - 9x^3 - 8x^2 + 15x \][/tex]
The correct answer is option C: [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex].
We want to multiply [tex]\((x^2 - 5x)\)[/tex] by [tex]\((2x^2 + x - 3)\)[/tex]. We will use distribution to expand the expression:
1. Distribute [tex]\(x^2\)[/tex]:
- [tex]\(x^2 \cdot 2x^2 = 2x^4\)[/tex]
- [tex]\(x^2 \cdot x = x^3\)[/tex]
- [tex]\(x^2 \cdot (-3) = -3x^2\)[/tex]
2. Distribute [tex]\(-5x\)[/tex]:
- [tex]\(-5x \cdot 2x^2 = -10x^3\)[/tex]
- [tex]\(-5x \cdot x = -5x^2\)[/tex]
- [tex]\(-5x \cdot (-3) = 15x\)[/tex]
Now, combine all these terms:
- [tex]\(2x^4\)[/tex]
- [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- [tex]\(15x\)[/tex]
So, the product is:
[tex]\[ 2x^4 - 9x^3 - 8x^2 + 15x \][/tex]
The correct answer is option C: [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex].
