Algebra Examples

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

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

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}

$\frac{1}{3}$ and

x^{4}

$x^{4}$ .

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

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

Step 1.2

Reorder

x^{3}

$x^{3}$ and

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

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

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

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

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

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

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

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

x^{3} \to 3

$x^{3} \to 3$

6 x \to 1

$6 x \to 1$

5 \to 0

$5 \to 0$

Step 2.2

The largest exponent is the degree of the polynomial.

4

$4$

4

$4$

Step 3

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

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

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

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}

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

Step 4.2

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

\frac{1}{3}

$\frac{1}{3}$

\frac{1}{3}

$\frac{1}{3}$

Step 5

List the results.

Polynomial Degree:

4

$4$

Leading Term:

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

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

Leading Coefficient:

\frac{1}{3}

$\frac{1}{3}$