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- 10 week duration
An introduction to numerical computation. Emphasis is placed on scientific and engineering notation, the rule of significant figures, and converting between SI and Imperial units.
Fractions, Percentage, Ratios and Proportion
Emphasis here is placed on understanding fractions, percent, and using ratios to compare quantities and set up proportions to solve problems.
Introduction to Algebra
Functions and Graphs
This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.
- Identify, measure, and calculate different types of straight lines and angles
- Calculate the interior angles of polygons
- Solve problems involving a variety of different types of triangles
- Calculate the area of a variety of different types of quadrilaterals
- Solve problems involving circles
- Calculate the areas and volumes of different solids
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.
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 factored-form 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. The trinomial factorability test is shown below: