Find out the answer to "Perform the indicated operations and indicate the degree..."

College
Algebra
College algebra
Transformations of functions

Stephanie Wilkerson

Answered question

2022-08-09

Perform the indicated operations and indicate the degree of the resulting polynomial.

(-8x^5+6x^2-9x+11)+(19x^5+3x^2-3x-14)

Answer & Explanation

alenahelenash

Expert2023-05-29Added 556 answers

To perform the indicated operations and indicate the degree of the resulting polynomial, we need to add the two polynomials together.
The given polynomials are:

(- 8 x^{5} + 6 x^{2} - 9 x + 11)

and

(19 x^{5} + 3 x^{2} - 3 x - 14)

.
To add these polynomials, we combine the like terms. Like terms are those that have the same variable raised to the same power.
Adding the coefficients of like terms, we get:

(- 8 x^{5} + 6 x^{2} - 9 x + 11) + (19 x^{5} + 3 x^{2} - 3 x - 14)

= (- 8 x^{5} + 19 x^{5}) + (6 x^{2} + 3 x^{2}) + (- 9 x - 3 x) + (11 - 14)

= 11 x^{5} + 9 x^{2} - 12 x - 3

The resulting polynomial after performing the addition is:

11 x^{5} + 9 x^{2} - 12 x - 3

.
Now, let's determine the degree of the resulting polynomial. The degree of a polynomial is the highest exponent of the variable.
In this case, the highest exponent is 5, which corresponds to the term

11 x^{5}

.
Therefore, the degree of the resulting polynomial is 5.

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