Quadratic Expressions

Factor a Perfect Square Trinomial

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…

Factor a Difference of Squares

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…

Factor Quadratics by Decomposition

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.…

Factor Quadratics by Trial-and-Error

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…

Common Factors

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 lesson. When you factor an expression, you’re making it more condensed. Let’s start with what factor means. Let’s…

Multiply Polynomials

A big part of converting quadratic equations from one form to another is the ability to multiply polynomials. A polynomial is a fancy term that describes an algebraic expression of 2 or more terms. For instance, 2x + 3 and 4xy + 3x + 5 are polynomials of 2 and…