Algebra Examples

$- \frac{w^{4}}{6} - 3 w^{2} + 10 w^{5}$

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

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Step 1.1

Move $- 3 w^{2}$ .

$- \frac{w^{4}}{6} + 10 w^{5} - 3 w^{2}$

Step 1.2

Reorder $- \frac{w^{4}}{6}$ and $10 w^{5}$ .

$10 w^{5} - \frac{w^{4}}{6} - 3 w^{2}$

Step 2

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

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Step 2.1

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

$10 w^{5} \to 5$

$- \frac{w^{4}}{6} \to 4$

$- 3 w^{2} \to 2$

Step 2.2

The largest exponent is the degree of the polynomial.

$5$

Step 3

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

$10 w^{5}$

Step 4

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

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Step 4.1

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

$10 w^{5}$

Step 4.2

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

$10$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $10 w^{5}$

Leading Coefficient: $10$