Question

what is the degree of this polynomial? $\frac{5}{7}y^{3}+5y^{2}+y + 1$
a. 3
b. 1
c. 2
d. 5

Explanation:

Step1: Recall the definition of the degree of a polynomial.

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial.

Step2: Identify the exponents of the variable \( y \) in each term.

• For the term \( \frac{5}{7}y^3 \), the exponent of \( y \) is \( 3 \).
• For the term \( 5y^2 \), the exponent of \( y \) is \( 2 \).
• For the term \( y \) (which can be written as \( y^1 \)), the exponent of \( y \) is \( 1 \).
• For the term \( 1 \) (which can be written as \( 1y^0 \)), the exponent of \( y \) is \( 0 \).

Step3: Determine the highest exponent.

Among the exponents \( 3 \), \( 2 \), \( 1 \), and \( 0 \), the highest one is \( 3 \).

Answer:

A. 3