Find the Degree, Leading Term, and Leading Coefficient y=-x(x+3)(x-3)

$y = - x (x + 3) (x - 3)$

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

Apply the distributive property.

$y = (- x \cdot x - x \cdot 3) (x - 3)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$y = (- (x \cdot x) - x \cdot 3) (x - 3)$

Multiply $x$ by $x$ .

$y = (- x^{2} - x \cdot 3) (x - 3)$

Multiply $3$ by $- 1$ .

$y = (- x^{2} - 3 x) (x - 3)$

Expand $(- x^{2} - 3 x) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$y = - x^{2} (x - 3) - 3 x (x - 3)$

Apply the distributive property.

$y = - x^{2} x - x^{2} \cdot - 3 - 3 x (x - 3)$

Apply the distributive property.

$y = - x^{2} x - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$y = - (x \cdot x^{2}) - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

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

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

$y = - (x \cdot x^{2}) - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

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

$y = - x^{1 + 2} - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

Add $1$ and $2$ .

$y = - x^{3} - x^{2} \cdot - 3 - 3 x \cdot x - 3 x \cdot - 3$

Multiply $- 3$ by $- 1$ .

$y = - x^{3} + 3 x^{2} - 3 x \cdot x - 3 x \cdot - 3$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$y = - x^{3} + 3 x^{2} - 3 (x \cdot x) - 3 x \cdot - 3$

Multiply $x$ by $x$ .

$y = - x^{3} + 3 x^{2} - 3 x^{2} - 3 x \cdot - 3$

Multiply $- 3$ by $- 3$ .

$y = - x^{3} + 3 x^{2} - 3 x^{2} + 9 x$

Subtract $3 x^{2}$ from $3 x^{2}$ .

$y = - x^{3} + 0 + 9 x$

Add $- x^{3}$ and $0$ .

$y = - x^{3} + 9 x$

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.

$- x^{3} \to 3$

$9 x \to 1$

The largest exponent is the degree of the polynomial.

$3$

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

$- x^{3}$

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.

$- 1$

List the results.

Polynomial Degree: $3$

Leading Term: $- x^{3}$

Leading Coefficient: $- 1$

Find the Degree, Leading Term, and Leading Coefficient y=-x(x+3)(x-3)

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