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