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Part III: For each polynomial, determine the degree and write the polynomial in descending order.

B. 2x5 + 14 – 3x4 + 7x + 3x3

2x5 – 3x4 +3x3 +7x + 14, degree 5

2x5 – 3x4 +3x3 +7x + 14, degree 2

14 +3x3 +7x – 3x4 + 2x5 , degree 3

– 3x4 +3x3 +7x + 14 + 2x5 , degree 4

1 answer

To determine the degree of the polynomial and write it in descending order, we analyze the given polynomial:

Polynomial: \(2x^5 + 14 - 3x^4 + 7x + 3x^3\)

  1. Sort the terms in descending order:

    • The highest degree term is \(2x^5\).
    • The second highest is \(-3x^4\).
    • The third highest is \(3x^3\).
    • The fourth highest is \(7x\).
    • The constant term is \(14\).

    Thus, in descending order, the polynomial becomes: \[ 2x^5 - 3x^4 + 3x^3 + 7x + 14 \]

  2. Determine the degree:

    • The degree of a polynomial is determined by the highest power of \(x\). In this case, the highest power is \(5\) from the term \(2x^5\).

Therefore, we can summarize the answer as:

Final Result:

  • Polynomial in Descending Order: \(2x^5 - 3x^4 + 3x^3 + 7x + 14\)
  • Degree: \(5\)

Based on the options provided:

  • Correct option: \[ 2x^5 - 3x^4 + 3x^3 + 7x + 14, \text{ degree } 5 \]

This option is correct.