Find the Degree, Leading Term, and Leading Coefficient g(n)=-(3n-1)(2n+1)

$g (n) = - (3 n - 1) (2 n + 1)$

Step 1

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

Simplify by multiplying through.

Apply the distributive property.

$g (n) = (- (3 n) + 1) (2 n + 1)$

Multiply.

Multiply $3$ by $- 1$ .

$g (n) = (- 3 n + 1) (2 n + 1)$

Multiply $- 1$ by $- 1$ .

$g (n) = (- 3 n + 1) (2 n + 1)$

Expand $(- 3 n + 1) (2 n + 1)$ using the FOIL Method.

Apply the distributive property.

$g (n) = - 3 n (2 n + 1) + 1 (2 n + 1)$

Apply the distributive property.

$g (n) = - 3 n (2 n) - 3 n \cdot 1 + 1 (2 n + 1)$

Apply the distributive property.

$g (n) = - 3 n (2 n) - 3 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$g (n) = - 3 \cdot (2 n \cdot n) - 3 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$g (n) = - 3 \cdot (2 (n \cdot n)) - 3 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

Multiply $n$ by $n$ .

$g (n) = - 3 \cdot (2 n^{2}) - 3 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

Multiply $- 3$ by $2$ .

$g (n) = - 6 n^{2} - 3 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

Multiply $- 3$ by $1$ .

$g (n) = - 6 n^{2} - 3 n + 1 (2 n) + 1 \cdot 1$

Multiply $2 n$ by $1$ .

$g (n) = - 6 n^{2} - 3 n + 2 n + 1 \cdot 1$

Multiply $1$ by $1$ .

$g (n) = - 6 n^{2} - 3 n + 2 n + 1$

Add $- 3 n$ and $2 n$ .

$g (n) = - 6 n^{2} - n + 1$

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.

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

$- n \to 1$

$1 \to 0$

The largest exponent is the degree of the polynomial.

$2$

Step 3

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

$- 6 n^{2}$

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.

$- 6 n^{2}$

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

$- 6$

Step 5

List the results.

Polynomial Degree: $2$

Leading Term: $- 6 n^{2}$

Leading Coefficient: $- 6$

Find the Degree, Leading Term, and Leading Coefficient g(n)=-(3n-1)(2n+1)

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