# Mathematics for Technology I (Math 1131)

Durham College, Mathematics
Free
• 55 lessons
• 1 quizzes
• 10 week duration
• ##### Numerical Computation

Here you'll be introduced to the bare basics of mathematics. Topics include commonly used words and phrases, symbols, and how to follow the order of operations.

• ##### Measurements

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.

• ##### Trigonometry with Right Triangles

Here we focus on right angle triangles within quadrant I of an x-y plane. None of the angles we evaluate here are greater than 90°. A unit on trigonometry with oblique triangles is covered later.

• ##### Trigonometry with Oblique Triangles

This unit is a continuation of trigonometry with right triangles except we'll extend our understanding to deal with angles *greater* than 90°. Resolving and combining vectors will be covered at the end of this unit.

• ##### Geometry

This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.

## Mathematics for Technology I (Math 1131)

### Simplify Expressions Through 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:

1. $\frac{ab+bc}{bc+bd}\phantom{\rule{0ex}{0ex}}$
2. $\frac{2{x}^{2}–5x–3}{4{x}^{2}–1}\phantom{\rule{0ex}{0ex}}$
3. $\frac{{x}^{2}–ax+2bx–2ab}{2{x}^{2}+ax–3{a}^{2}}\phantom{\rule{0ex}{0ex}}$

At first glance, you might be questioning how do I divide two polynomials when we’ve only learned how to divide polynomials with monomials? Factoring the numerator and denominator separately should always be considered as an option before devising other plans or giving up. By converting polynomials into factors, you open up the opportunity to cancel with similar factors in the other polynomial, as you’ll see below.

Question: Simplify each expression shown above.

 $\frac{ab+bc}{bc+bd}=\frac{b\left(a+c\right)}{b\left(c+d\right)}⇒\frac{\overline{)b}\left(a+c\right)}{\overline{)b}\left(c+d\right)}⇒\frac{\mathbf{a}\mathbf{+}\mathbf{c}}{\mathbf{c}\mathbf{+}\mathbf{d}}\phantom{\rule{0ex}{0ex}}$ ✔ Technique: Common factor both the numerator and denominator. $\frac{2{x}^{2}–5x–3}{4{x}^{2}–1}=\frac{\left(2x+1\right)\left(x-3\right)}{\left(2x–1\right)\left(2x+1\right)}⇒\frac{\overline{)\left(2x+1\right)}\left(x-3\right)}{\left(2x–1\right)\overline{)\left(2x+1\right)}}=\frac{\mathbf{x}\mathbf{–}\mathbf{3}}{\mathbf{2}\mathbf{x}\mathbf{–}\mathbf{1}}\phantom{\rule{0ex}{0ex}}$ ✔ Technique: The numerator is factored by decomposition; the denominator is a difference of squares. $\frac{{x}^{2}–ax+2bx–2ab}{2{x}^{2}+ax–3{a}^{2}}=\phantom{\rule{0ex}{0ex}}\frac{x\left(x–a\right)+2b\left(x–a\right)}{x\left(2x+3a\right)–a\left(2x+3a\right)}=\phantom{\rule{0ex}{0ex}}\frac{\left(x+2b\right)\left(x–a\right)}{\left(x–a\right)\left(2x+3a\right)}=\frac{\left(x+2b\right)\overline{)\left(x–a\right)}}{\overline{)\left(x–a\right)}\left(2x+3a\right)}=\frac{\mathbf{x}\mathbf{+}\mathbf{2}\mathbf{b}}{\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{3}\mathbf{a}}\phantom{\rule{0ex}{0ex}}$ ✔ Technique: Factor the numerator by grouping; the denominator is factored by decomposition.