Find the Degree, Leading Term, and Leading Coefficient y=x(x^2-5)

$y = x (x^{2} - 5)$

Step 1

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

Apply the distributive property.

$y = x \cdot x^{2} + x \cdot - 5$

Multiply $x$ by $x^{2}$ by adding the exponents.

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$y = x \cdot x^{2} + x \cdot - 5$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = x^{1 + 2} + x \cdot - 5$

Add $1$ and $2$ .

$y = x^{3} + x \cdot - 5$

Move $- 5$ to the left of $x$ .

$y = x^{3} - 5 x$

Step 2

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

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

$x^{3} \to 3$

$- 5 x \to 1$

The largest exponent is the degree of the polynomial.

$3$

Step 3

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

$x^{3}$

Step 4

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

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

$x^{3}$

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

$1$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $x^{3}$

Leading Coefficient: $1$