Summary of Steps to Factor Quadratic Trinomials

Solving a quadratic (or any kind of equation) by factoring it makes use of a principle known as the zero-product rule. Zero Product Rule If ab = 0 then either a = 0 or b = 0 (or both). In other words, if the product of two things is zero then one of those two things must be zero, because the only way…

The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, like how many sheep a farmer owns. These are called the natural numbers, or sometimes the counting numbers. Natural Numbers or “Counting Numbers” 1, 2, 3, 4, 5, . ….

he solutions to a quadratic equation can be found directly from the quadratic formula. The equation ax2 + bx + c = 0 has solutions The advantage of using the formula is that it always works. The disadvantage is that it can be more time-consuming than some of the methods previously discussed. As a general rule you should look…

Another method for factoring these kinds of quadratic trinomials is called factoring by grouping. Factoring by grouping can be a bit more tedious and is often not worth the trouble if you can find the correct factors by some quick trial and error. However, it works quite well when the factors are not immediately obvious,…

General Strategy Recall the general strategy for setting up word problems. Refer to the Problem Solving Strategies page for more detail. Read the problem carefully: Determine what is known, what is unknown, and what question is being asked. Represent unknown quantities in terms of a variable. Use diagrams where appropriate. Find formulas or mathematical relationships…

A system of equations refers to a number of equations with an equal number of variables. We will only look at the case of two linear equations in two unknowns. The situation gets much more complex as the number of unknowns increases, and larger systems are commonly attacked with the aid of a computer. A…