Find the Degree, Leading Term, and Leading Coefficient f(x)=x(x-3)^2

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

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

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$f (x) = x ((x - 3) (x - 3))$

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$f (x) = x (x (x - 3) - 3 (x - 3))$

Apply the distributive property.

$f (x) = x (x \cdot x + x \cdot - 3 - 3 (x - 3))$

Apply the distributive property.

$f (x) = x (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 3$ to the left of $x$ .

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

Multiply $- 3$ by $- 3$ .

$f (x) = x (x^{2} - 3 x - 3 x + 9)$

Subtract $3 x$ from $- 3 x$ .

$f (x) = x (x^{2} - 6 x + 9)$

Apply the distributive property.

$f (x) = x \cdot x^{2} + x (- 6 x) + x \cdot 9$

Simplify.

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

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

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

$f (x) = x \cdot x^{2} + x (- 6 x) + x \cdot 9$

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

$f (x) = x^{1 + 2} + x (- 6 x) + x \cdot 9$

Add $1$ and $2$ .

$f (x) = x^{3} + x (- 6 x) + x \cdot 9$

Rewrite using the commutative property of multiplication.

$f (x) = x^{3} - 6 x \cdot x + x \cdot 9$

Move $9$ to the left of $x$ .

$f (x) = x^{3} - 6 x \cdot x + 9 \cdot x$

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

Move $x$ .

$f (x) = x^{3} - 6 (x \cdot x) + 9 \cdot x$

Multiply $x$ by $x$ .

$f (x) = x^{3} - 6 x^{2} + 9 \cdot x$

$f (x) = x^{3} - 6 x^{2} + 9 x$

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.

$x^{3} \to 3$

$- 6 x^{2} \to 2$

$9 x \to 1$

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 f(x)=x(x-3)^2

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