High School

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Perform the indicated operations and write the resulting polynomial in standard form:

\((6x^7 + 3x^5 + 3x) + (8x^7 + 5x^5 - 7x)\)

A. \(14x^7 + 8x^5 - 4x\)

B. \(14x^7 + 8x^5 - 4x^2\)

C. \(14x^7 + 8x^5 - 10x\)

D. \(14x^7 + 8x^5 - 4\)

Answer :

Final answer:

To solve the question, we combine like terms to get the resulting polynomial in standard form: 14x^7 + 8x^5 - 4x (option c).

Explanation:

The student is tasked with performing the indicated operations and writing the resulting polynomial in standard form after combining like terms from the given polynomials (6x7+3x5+3x) and (8x7+5x5-7x). To solve this, we simply add the coefficients of the like terms:

  • Combine x7 terms: 6x7 + 8x7 = 14x7
  • Combine x5 terms: 3x5 + 5x5 = 8x5
  • Combine x terms: 3x - 7x = -4x

The resulting polynomial in standard form is 14x7 + 8x5 - 4x.

The correct answer is: (c) 14x7 + 8x5 - 4x

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