Find the Degree, Leading Term, and Leading Coefficient y=5x^2-3x^3+6x-12x^7-3

$y = 5 x^{2} - 3 x^{3} + 6 x - 12 x^{7} - 3$

Step 1

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

Move $6 x$ .

$y = 5 x^{2} - 3 x^{3} - 12 x^{7} + 6 x - 3$

Move $5 x^{2}$ .

$y = - 3 x^{3} - 12 x^{7} + 5 x^{2} + 6 x - 3$

Reorder $- 3 x^{3}$ and $- 12 x^{7}$ .

$y = - 12 x^{7} - 3 x^{3} + 5 x^{2} + 6 x - 3$

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.

$- 12 x^{7} \to 7$

$- 3 x^{3} \to 3$

$5 x^{2} \to 2$

$6 x \to 1$

$- 3 \to 0$

The largest exponent is the degree of the polynomial.

$7$

Step 3

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

$- 12 x^{7}$

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.

$- 12 x^{7}$

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

$- 12$

Step 5

List the results.

Polynomial Degree: $7$

Leading Term: $- 12 x^{7}$

Leading Coefficient: $- 12$