College Algebra Formulas & Examples

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  • 0:04 Working with Exponents
  • 2:15 Multiplying Polynomials
  • 3:23 Factoring Polynomials
  • 4:21 The Quadratic Formula
  • 5:26 Lesson Summary
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Lesson Transcript
Instructor: Laura Golnabi

Laura Golnabi is a Ph.D. student in Mathematics Education at Teachers College, Columbia University. She also teaches undergraduate mathematics courses, and has developed problem solving courses designed for non-STEM majors. Her current research involves if and when students suffering from mathematics anxiety are able to have positive, flow-like experiences in mathematics.

In this lesson, you will be introduced to some of the most commonly used formulas in a college algebra course. Also, you will get to see some examples that use the formulas.

Working with Exponents

First, recall that an exponent term is composed of a base and an exponent. For example, the term x2 has base x, and exponent 2.

Now, when working with exponents, here are some of the most commonly used formulas and corresponding examples:

Product Rule: When multiplying two exponents, you should add the exponents.

xa * xb = xa+b

Example: x2 * x3 = x2+3 = x5

Quotient Rule: When dividing two exponents, you should subtract the exponents.

xa / xb = xa-b

Example: x5 / x2 = x5-2 = x3

Power to a Power Rule: When raising an exponent to another exponent, multiply the exponents.

(xa)b = xa*b

Example: (x2)3 = x2*3 = x6

Zero Exponent Rule: Any base raised to the power 0 is equal to 1.

x0 = 1

Example: 120 = 1

Power of a Product Rule: When raising a product to the same exponent, each base in the product is raised to that exponent.

(x*y)a = xa * ya

Example: (x*y)2 = x2 * y2

Power of a Quotient Rule: When raising a quotient to the same exponent, each base in the quotient is raised to that exponent.

(x / y)a = xa / ya

Example: (x / y)2 = x2 / y2

That's a lot of rules isn't it? Don't worry, if you're a little overwhelmed, go back and give them a second look. They are all pretty self-explanatory and do a good job of standing out from one another.

Multiplying Polynomials

To multiply two polynomials, you should multiply each term in the first polynomial by each term in the second polynomial.

In general terms, this is what the formula looks like:

(a + b)(c + d) = a*c + a*d + b*c + b*d

Note, that you may have also heard of this process being called FOIL which stands for First (multiply first terms in each polynomial), Out (multiply outer terms), In (multiply inner terms), Last (multiply last terms in each polynomial).

Here's an example to clarify this a bit:

(3x + 2)(4x + 5) = 3x*4x + 3x*5 + 2*4x + 2*5

Simplifying the right side using the rules of exponents we just reviewed, we have:

3x*4x + 3x*5 + 2*4x + 2*5 = 12x2 + 15x + 8x + 10 =12x2 + 23x + 10

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