Middle School

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Multiply the following expression:

\[(x^2 - 5x)(2x^2 + x - 3)\]

Choose the correct option:

A. \[2x^4 - 9x^3 - 8x^2 + 15x\]

B. \[2x^4 - 9x^3 - 9x^2 - 15x\]

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

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

Answer :

Final answer:

The correct answer is 'A', 2x⁴ - 9x³ - 8x² + 15x. This is obtained by multiplying each term in the first bracket by every term in the second bracket, and then simplifying.

Explanation:

To solve this problem, we will multiply each term in the first bracket by every term in the second bracket. Also remember to follow the rules of sign when multiplying. For example, positive multiplied by negative equals negative, and negative multiplied by negative equals positive.

  1. First, multiply x² by each term in the second bracket: 2x²*x² + x*x² - 3*x² to get 2x⁴ + x³ - 3x².
  2. Next, multiply -5x by each term in the second bracket: -5x*2x² + -5x*x + -5x * -3 to get -10x³ - 5x² + 15x.

Combine these two sets of products to form the answer: (2x⁴ + x³ - 3x²) + (-10x³ - 5x² + 15x) which simplifies to

2x⁴ - 9x³ - 8x² + 15x.

Therefore, the correct answer is 'A'. Any option besides 'A' is incorrect because of incorrect multiplication or simplification of terms.

Learn more about Polynomial Multiplication here:

https://brainly.com/question/20121808

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