High School

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Multiply:

[tex]\left(x^2-5x\right)\left(2x^2+x-3\right)[/tex]

A. [tex]2x^4-9x^3-9x^2-15x[/tex]

B. [tex]2x^4+9x^3-8x^2+15x[/tex]

C. [tex]2x^4-9x^3-8x^2+15x[/tex]

D. [tex]4x^4+9x^3-8x^2+15x[/tex]

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].

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