Algebra Examples

$x^{3} + \frac{1}{3} x^{4} + 6 x + 5$

Step 1

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

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Step 1.1

Combine $\frac{1}{3}$ and $x^{4}$ .

$x^{3} + \frac{x^{4}}{3} + 6 x + 5$

Step 1.2

Reorder $x^{3}$ and $\frac{x^{4}}{3}$ .

$\frac{x^{4}}{3} + x^{3} + 6 x + 5$

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.

$\frac{x^{4}}{3} \to 4$

$x^{3} \to 3$

$6 x \to 1$

$5 \to 0$

Step 2.2

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.

$\frac{x^{4}}{3}$

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.

$\frac{x^{4}}{3}$

Step 4.2

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

$\frac{1}{3}$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $\frac{x^{4}}{3}$

Leading Coefficient: $\frac{1}{3}$