Question

What is the degree of each polynomial?

a. −w^0 Degree: 0
b. 36x^8−2x^9 + 8x^7 Degree: 9
c. rs^3 + xy^7 Degree: 2
d. 3x^4 + 9x^3 − 4x^5 + 1 Degree: 5

Answer 1

The degree of a polynomial is the highest exponent of a variable term in the polynomial. Given the polynomials, their degrees are 0, 9, 10, and 5 respectively.

Step-by-step explanation:

The degree of a polynomial is the highest exponent of the variable in its terms when the polynomial is expressed in its standard form (i.e., terms are ordered from highest to lowest degree). Here are the degrees of the given polynomials:

1. −w^0 has a degree of 0 since any number to the power of 0 is 1, which is a constant.
2. 36x^8 − 2x^9 + 8x^7 has a degree of 9 because the highest exponent of x in the polynomial is 9.
3. rs^3 + xy^7 is not a single-variable polynomial, so its degree is found by adding the exponents of the variables in each term and then taking the highest sum, which in this case is 10 (s^3 has a degree of 3, and y^7 has a degree of 7).
4. 3x^4 + 9x^3 − 4x^5 + 1 has a degree of 5 since the highest exponent of x in the polynomial is 5.