How to Decompose Partial Fractions
A process called partial fractions takes one fraction and expresses it as the sum or difference of two other fractions. In calculus, this process is useful before you integrate a function. Because integration [more…]
How to Factor a Polynomial Expression
In mathematics, factorization or factoring is the breaking apart of a polynomial into a product of other smaller polynomials. If you choose, you could then multiply these factors together, and you should [more…]
How to Use the Roots of a Polynomial to Find Its Factors
The factor theorem states that you can go back and forth between the roots of a polynomial and the factors of a polynomial. If you know one, in other words, you know the other. At times, your teacher or [more…]
How to Complete the Square
Completing the square comes in handy when you’re asked to solve an unfactorable quadratic equation and when you need to graph conic sections. Follow these steps to solve the equation [more…]
How to Solve Linear Systems
When you solve systems with two variables and therefore two equations, the equations can be linear or nonlinear. Linear systems are usually expressed in the form Ax + By [more…]
How to Solve Systems that Have More than Two Equations
Larger systems of linear equations involve more than two equations that go along with more than two variables. These larger systems can be written in the form Ax + By + Cz + . . . [more…]
How to Solve Nonlinear Systems
In a nonlinear system, at least one equation will have a graph that isn’t a straight line. You can always write a linear equation in the form Ax + By = C [more…]
Even-Odd Identities in Trigonometric Functions
All functions, including trig functions, can be described as being even, odd, or neither. Knowing whether a trig function is even or odd can help you simplify an expression. These even-odd identities are [more…]
Completing the Square for Conic Sections
When the equation of a conic section isn't written in its standard form, completing the square is the only way to convert the equation to its standard form. The steps of the process are as follows: [more…]
Finding the Key Parts of All Hyperbolas
A hyperbola is the set of all points in the plane such that the difference of the distances from two fixed points (the foci) is a positive constant. Hyperbolas always come in two parts, and each one is [more…]
Rules for Adding and Subtracting Matrices
To add or subtract matrices, you have to operate on their corresponding elements. In other words, you add or subtract the first row/first column in one matrix to or from the exact same element in another [more…]
Logarithm Basics
Logarithms are simply another way to write exponents. Exponential and logarithmic functions are inverses of each other. For solving and graphing logarithmic functions [more…]
