- 34 lessons
- 0 quizzes
- 7 week duration
Unit 1: Linear Systems
Unit 2: Analytic Geometry
Unit 3: Geometric Properties
Unit 4: Quadratic Relations
Most relations that you have studied in mathematics have been linear. However, many non-linear also exist in real life.
Unit 5: Quadratic Expressions
Unit 6: Quadratic Equations
Unit 7: Trigonometry
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 x coordinates of the roots.
The first technique you can try is trial-and-error.
Take, for example, the quadratic equation:
x² – x – 6 = 0
First, identify the c constant and b coefficients. The c constant is -6, the b coefficient it -1. You have to do this all the time.
Next, you need to find two factors of -6 that multiply to it, and those same two factors add to -1.
The only possibility that words is -3 and +2.
-3 × (+2) = -6
-3 + 2 = -1
You then rewrite your equation as two factors: y = (x – 6)(x – 1).
Pointers to keep in mind:
- Always begin the process of factoring a quadratic by common factoring if possible. In the example shown above, nothing could be common factored.
- This technique can only be tried if the a coefficient is 1. Otherwise, another technique known as factoring by decomposition is used (next lesson).
- Many quadratic expressions, such as x² + 3x + 5, cannot be factored over the integers. No two integers have a product of 5 and a sum of 3. In that case, we’ll use the quadratic formula (more to come on this later on).
Now let’s see this in action.