 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 nonlinear also exist in real life.

Unit 5: Quadratic Expressions

Unit 6: Quadratic Equations

Unit 7: Trigonometry
Factor Quadratics by Decomposition
When a general form quadratic has an a coefficient greater than 1, the trialanderror 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.
Arguably you could common factor the 3, leaving x² with a coefficient of 1:
y = 3 ( x² + 5/3x + 2 )
But then you’re left with finding two factors of 2 that add to 5/3!
To factor quadratics whose a > 1, we use a technique known as factoring by decomposition, which involving breaking up the middle term – hence the name.
Let’s see a few examples of this technique in action.
To summarize, factoring by decomposition involves finding two integers whose product is a × c and whose sum is b. Then, break up the middle term and factor by grouping.
Interestingly, referring back to the initial equation:
y = 3x² + 5x + 6
If you try factoring by decomposition here, it still won’t yield a factoredform quadratic. In that case, you’d have to use the quadratic formula to find the roots (more on this to come). Therefore, not all quadratic expressions of the form ax² + bx + c can be factored over the integers.