# Glossary for College Algebra Lesson 3: Polynomials

### Polynomial

An expression made up of variables and/or constants that are combined with addition, subtraction, and multiplication.  Examples: -3x+4, 6y^4+7y^2-8y+13, 5xy^2z-11

### Degree of a Polynomial

To find the degree of a polynomial, we first need to find the degree of each of its terms.  The degree of a term is the sum of the powers of all of the variables in that term.  So, for instance, 7x^2 has a degree of 2, and -4xy^2z has a degree of 4.  The degree of a polynomial is equal to the degree of its highest-degree term.  Examples: 6y^4+7y^2-8y+13 has a degree of 4 or, in other words, is a fourth degree polynomial.

### Standard Form of a Polynomial

A polynomial is said to be in standard form when it is written with its highest-degree term first, with the rest of the terms written in order of descending degree.  For example, 6y^4+7y^2-8y+13 is written in standard form, whereas 7y^2-8y+13+6y^4 is not.

### Exponent

Repeated multiplication can be written using exponential notation.  For example, 3\cdot3\cdot3\cdot3\cdot3=3^5.  Here, the number 3 is known as the base, and 5 is known as the exponent or the power.  The base thus refers to the quantity being multiplied by itself, and the exponent tells us how many times this multiplication happens.

### Distributive Property

For an expression of the form a(b+c), we can say that a(b+c)=ab+ac In words, the distributive property says that if an entire expression is multiplied by some quantity, that quantity multiplies each and every term in the expression.
Examples:

3(2-7)=3(2)+3(-7)=6-21=-15
-4x^2(x^2+3x-2)=(-4x^2)(x^2)+(-4x^2)(3x)+(-4x^2)(-2x)=-4x^4-12x^3+8x^2
(x+3)(2x-1)=(x+3)(2x)+(x+3)(-1)=(2x)(x+3)+(-1)(x+3)=2x(x)+2x(3)-x-3=2x^2+6x-x-3=2x^2+5x-3