Find the Degree, Leading Term, and Leading Coefficient 5y^4+y^3+2/3y^2+y+1

$5 y^{4} + y^{3} + \frac{2}{3} y^{2} + y + 1$

Step 1

Combine $\frac{2}{3}$ and $y^{2}$ .

$5 y^{4} + y^{3} + \frac{2 y^{2}}{3} + y + 1$

Step 2

The degree of a polynomial is the highest degree of its terms.

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$5 y^{4} \to 4$

$y^{3} \to 3$

$\frac{2 y^{2}}{3} \to 2$

$y \to 1$

$1 \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 3

The leading term in a polynomial is the term with the highest degree.

$5 y^{4}$

Step 4

The leading coefficient of a polynomial is the coefficient of the leading term.

The leading term in a polynomial is the term with the highest degree.

$5 y^{4}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$5$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $5 y^{4}$

Leading Coefficient: $5$