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

$(x^{2} + 2 x) (x - 3)$

Step 1

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

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

Apply the distributive property.

$x^{2} (x - 3) + 2 x (x - 3)$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

Move $- 3$ to the left of $x^{2}$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $2$ .

$x^{3} - 3 x^{2} + 2 x^{2} - 6 x$

Add $- 3 x^{2}$ and $2 x^{2}$ .

$x^{3} - x^{2} - 6 x$

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.

$x^{3} \to 3$

$- x^{2} \to 2$

$- 6 x \to 1$

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: $1$

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

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