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Answer :
Sure! Let's multiply the polynomials [tex]\((x^2 - 5x)(2x^2 + x - 3)\)[/tex] step by step.
1. Distribute each term in the first polynomial to each term in the second polynomial:
- First term from the first polynomial: [tex]\(x^2\)[/tex]
- Multiply [tex]\(x^2 \times 2x^2 = 2x^4\)[/tex]
- Multiply [tex]\(x^2 \times x = x^3\)[/tex]
- Multiply [tex]\(x^2 \times (-3) = -3x^2\)[/tex]
- Second term from the first polynomial: [tex]\(-5x\)[/tex]
- Multiply [tex]\(-5x \times 2x^2 = -10x^3\)[/tex]
- Multiply [tex]\(-5x \times x = -5x^2\)[/tex]
- Multiply [tex]\(-5x \times (-3) = 15x\)[/tex]
2. Combine all the resulting terms:
[tex]\(2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x\)[/tex]
3. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
Therefore, the combined expression is:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
So, the correct answer is A. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex]
1. Distribute each term in the first polynomial to each term in the second polynomial:
- First term from the first polynomial: [tex]\(x^2\)[/tex]
- Multiply [tex]\(x^2 \times 2x^2 = 2x^4\)[/tex]
- Multiply [tex]\(x^2 \times x = x^3\)[/tex]
- Multiply [tex]\(x^2 \times (-3) = -3x^2\)[/tex]
- Second term from the first polynomial: [tex]\(-5x\)[/tex]
- Multiply [tex]\(-5x \times 2x^2 = -10x^3\)[/tex]
- Multiply [tex]\(-5x \times x = -5x^2\)[/tex]
- Multiply [tex]\(-5x \times (-3) = 15x\)[/tex]
2. Combine all the resulting terms:
[tex]\(2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x\)[/tex]
3. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
Therefore, the combined expression is:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
So, the correct answer is A. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex]
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