The Handy Math Answer Book

What are quartic equations?

Quartic equations are polynomial equations whose highest power of the unknown
variable is four. Put another way, quartic equations are algebraic equations whose
highest exponent (or degree or order) is four. (For more about the history of solving
quartic [and cubic] equations, see “History of Mathematics.”) But take note: Quartic
equations are notthe same as quadratic equations—or second degree equations in
one variable—so don’t mix them up.

What are the names of polynomial equationswith different degrees?

The polynomial equations with different degrees (or orders)—especially the lowest
degrees—are as follows:

• first degree(1) polynomial linear


• second degree(2) polynomial quadratic


• third degree(3) polynomial cubic


• fourth degree(4) polynomial quartic


• fifth degree(5) polynomial quintic


• sixth degree(6) polynomial sextic

How do you multiply polynomial equations?

To multiply two monomials, multiply the coefficients and then multiply the variables
(and when multiplying the variables, keep the variables and add the exponents). The
following are several examples of multiplying various polynomial equations:

Multiplying monomials:

(5x)(6x^2 )

(5 6)(x^2 ^1 ) (multiply the numbers and add the exponents)

 30 x^3

Multiplying a monomial and polynomial (binomial):

4 y(2y8)

 4 y(2y)  4 y(8) (multiply 4ytimes both terms)

 8 y^2  32 y(depending on what is on the other side of the equation, you can

further simplify by dividing by 8, or y^2  4 y)

Multiplying polynomials:

6 y^3 (8y^6  5 y^4  3 y^3 )

 6 y^3 (8y^6 )  6 y^3 (5y^4 )  6 y^3 (3y^3 )

 48 y^9  30 y^7  18 y^6151

ALGEBRA