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

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

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

Apply the distributive property.

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

Combine $\frac{3}{2}$ and $x$ .

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$f (x) = \frac{3 x}{2} + \frac{3}{2} \cdot (2 (- 1))$

Cancel the common factor.

$f (x) = \frac{3 x}{2} + \frac{3}{2} \cdot (2 \cdot - 1)$

Rewrite the expression.

$f (x) = \frac{3 x}{2} + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

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

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.

$\frac{3 x}{2} \to 1$

$- 3 \to 0$

The largest exponent is the degree of the polynomial.

$1$

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

$\frac{3 x}{2}$

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.

$\frac{3 x}{2}$

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

$\frac{3}{2}$

List the results.

Polynomial Degree: $1$

Leading Term: $\frac{3 x}{2}$

Leading Coefficient: $\frac{3}{2}$