Precalculus Examples

$z x + 5 x^{2} z - z^{5}$

Step 1

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

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Step 1.1

Reorder $z$ and $x$ .

$x z + 5 x^{2} z - z^{5}$

Step 1.2

Move $x z$ .

$5 x^{2} z - z^{5} + x z$

Step 1.3

Reorder $5 x^{2} z$ and $- z^{5}$ .

$- z^{5} + 5 x^{2} z + x z$

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.

$- z^{5} \to 5$

$5 x^{2} z \to 3$

$x z \to 2$

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.

$- z^{5}$

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.

$- z^{5}$

Step 4.2

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

$- 1$

Step 5

List the results.

Polynomial Degree: $5$

Leading Term: $- z^{5}$

Leading Coefficient: $- 1$