Find the Degree, Leading Term, and Leading Coefficient (2a-5)(a^2-1)

$(2 a - 5) (a^{2} - 1)$

Step 1

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

Expand $(2 a - 5) (a^{2} - 1)$ using the FOIL Method.

Apply the distributive property.

$2 a (a^{2} - 1) - 5 (a^{2} - 1)$

Apply the distributive property.

$2 a \cdot a^{2} + 2 a \cdot - 1 - 5 (a^{2} - 1)$

Apply the distributive property.

$2 a \cdot a^{2} + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

Simplify terms.

Simplify each term.

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

Move $a^{2}$ .

$2 (a^{2} a) + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

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

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

$2 (a^{2} a^{1}) + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

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

$2 a^{2 + 1} + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

Add $2$ and $1$ .

$2 a^{3} + 2 a \cdot - 1 - 5 a^{2} - 5 \cdot - 1$

Multiply $- 1$ by $2$ .

$2 a^{3} - 2 a - 5 a^{2} - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$2 a^{3} - 2 a - 5 a^{2} + 5$

Move $- 2 a$ .

$2 a^{3} - 5 a^{2} - 2 a + 5$

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.

$2 a^{3} \to 3$

$- 5 a^{2} \to 2$

$- 2 a \to 1$

$5 \to 0$

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.

$2 a^{3}$

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.

$2 a^{3}$

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

$2$

Step 5

List the results.

Polynomial Degree: $3$

Leading Term: $2 a^{3}$

Leading Coefficient: $2$

Find the Degree, Leading Term, and Leading Coefficient (2a-5)(a^2-1)

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