Precalculus Examples

$x^{5} - 4 x^{2} + 9$

Step 1

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

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Step 1.1

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

$x^{5} \to 5$

$- 4 x^{2} \to 2$

$9 \to 0$

Step 1.2

The largest exponent is the degree of the polynomial.

$5$

Step 2

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

$x^{5}$

Step 3

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

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Step 3.1

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

$x^{5}$

Step 3.2

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

$1$

Step 4

List the results.

Polynomial Degree: $5$

Leading Term: $x^{5}$

Leading Coefficient: $1$

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