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Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.

(5x^2-8x-1) + (2^2-3x+5) - (x^2-5x-3)
(Simplify your answer. Type your answer in standard​ form.)

The degree of the resulting polynomial is blank.
(Type a whole​ number.)

1 answer

To perform the indicated operations on the polynomials, we will first rewrite the second polynomial \( (2^2 - 3x + 5) \) correctly and then combine all the terms.

  1. Rewrite the polynomials:
    • First polynomial: \( 5x^2 - 8x - 1 \)
    • Second polynomial: \( 2^2 - 3x + 5 \) simplifies to \( 4 - 3x + 5 \), which can be rewritten as \( -3x + 9 \).
    • Third polynomial: \( -(x^2 - 5x - 3) \) simplifies to \( -x^2 + 5x + 3 \).

Now, we combine the three polynomials: \[ (5x^2 - 8x - 1) + (-3x + 9) + (-x^2 + 5x + 3) \]

  1. Combine all the like terms:
    • \( 5x^2 - x^2 = 4x^2 \)
    • \( -8x - 3x + 5x = -6x \)
    • \( -1 + 9 + 3 = 11 \)

So, the resulting polynomial is: \[ 4x^2 - 6x + 11 \]

  1. Write it in standard form: The polynomial in standard form is: \[ 4x^2 - 6x + 11 \]

  2. Determine the degree: The degree of the polynomial is the highest power of \( x \) present, which in this case is: \[ \text{Degree} = 2 \]

Thus, the final answer is:

  • The polynomial: \( 4x^2 - 6x + 11 \)
  • The degree: \( 2 \)