Find the Degree, Leading Term, and Leading Coefficient 12x^9+x^8+2x^4+25x^2+x+27

$12 x^{9} + x^{8} + 2 x^{4} + 25 x^{2} + x + 27$

Step 1

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.

$12 x^{9} \to 9$

$x^{8} \to 8$

$2 x^{4} \to 4$

$25 x^{2} \to 2$

$x \to 1$

$27 \to 0$

The largest exponent is the degree of the polynomial.

$9$

Step 2

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

$12 x^{9}$

Step 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.

$12 x^{9}$

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

$12$

Step 4

List the results.

Polynomial Degree: $9$

Leading Term: $12 x^{9}$

Leading Coefficient: $12$