Factoring

The skills you’ll learn in this lesson will come in handy unexpectedly one day when you’re stuck trying to simplify what appears to be an impossible expression to reduce. Take a look at the three expressions below: null null null At first glance, you might be questioning how do I…

Although this concepts was briefly discussed in one of the earlier lessons, you learned that sometimes you may need to combine several of the techniques to factor a single expression. As a result, to factor the expressions found in this section, you’ll have to device a plan before starting because…

Generally, the higher the degree of a polynomial, the harder it becomes to factor. The highest degree you’re expected to factor in this course are cubic equation (those raised to the power of three). Specifically, we’ll look at examples similar in structure to quadratics that are a difference of square,…

In this unit’s final lesson, we’ll learn how to quickly factor general form quadratics that are considered “perfect square trinomials” (PST). In a PST, the first and last term of these trinomials are always perfect squares. If you don’t recognize the pattern of a PST, you could still factor the quadratic…

When a general form quadratic has an a coefficient greater than 1, the trial-and-error method no longer works. Take, for example, the equation: y = 3x² + 5x + 6 You can’t choose 3 and 2 as factors that multiply to 6 and add to 5 – it doesn’t work that way.…

For the first time in this course, you’ll learn how to convert a quadratic that’s in its general form to a quadratic in factored form. General form: y = ax² + bx + c   → Factored form:  y = a(x – r)(x – s)   where r and s represent the…

So far we’ve learned three factoring techniques. The first one, common factoring, is a technique that can be used for any polynomial. The other two were specific for quadratics, namely trial-and-error and decomposition. The whole purpose behind factoring any quadratic – if you haven’t discovered already – is convert it in…

Another major part of algebra and converting quadratics into different forms is the ability to common factor. Think of this as the opposite of “expanding”, which is what we did in in the previous unit. When you factor an expression, you’re making it more condensed. Let’s start with what factor means. Let’s…