WARNING: Excuses incoming….
This week was not the successful week I envisioned. Up to this point, I’ve managed to get a minimum of 5 hours of work done on Khan Academy every seven days. This week I think I got 3…
Excuses: I spent all of Monday driving from Toronto to Stratford (my hometown) and back again that night for Thanksgiving. I went on two dates on Tuesday and Thursday morning and spent all of Wednesday reading the latest issue of Bloomberg Businessweek (my New Year’s resolution was to read every issue this year by midnight on Wednesdays). Finally, a friend crashed on my couch from Friday to Sunday which made it difficult to get any work done while we were drinking beer and watching hockey.
That said, I did manage to get some work done on the unit Quadratics and Polynomials. I think I must have missed a lesson on polynomials as the unit got straight into them but I didn’t have any clue what a polynomial was. As far I can tell, “polynomial” seems to be an umbrella term that includes monomials, binomials, trinomials and, I believe, quadratics. I’m not 100% certain, but I believe the definitions of each are:
- Monomial: a term on its own containing one variable (ex. 3xy)
- Binomial: an expression with two terms/variables (ex. 3x + 4)
- Trinomial: an expression with three terms/variable (ex. x^2 + 5x – 2)
- Polynomial: an umbrella term used for an expression with two (? – might be more than two) terms/variables (ex. –w^3 + 8w^2 + w +4)
- Quadratic: an expression with at least one term that is to the power of 2 or more (ex. 3x^2 + 5 or 3x^3 + 5)
- As far as I’ve come to understand, polynomials and quadratics typically contain at least one variable that is to the power of 2 or greater.
The unit started off by adding and subtracting like terms in polynomials, including variables to the power of 2, 3, etc. I found out adding and subtracting variables with exponents in a polynomial is the same as adding variables in expressions that are exponent-less; You can only add and subtract terms that have the same variable AND are to the same power (ex. (2x^4 + x^2 – 4) + (3x^2 + 5) = 2x^4 + 4x^2 + 1). When subtracting polynomials, you simply multiply the polynomial being subtracted by -1 in order to add them together (ex. (3x^2 + 5) – (x^2 -4) = (3x^2 + 5) + (-1) (x^2 -4) = (3x^2 + 5) + (-x^2 + 4) = 2x^2 + 9).
The next section worked on multiplying binomials using the distributive property (ex. (x – 2)(x – 6) = x^2 – 6x – 2x + 12). Lastly, going through this section of the unit, I learned there are a couple key equations to remember:
- (x + a)(x – a) = x^2 – a^2
- (x + a)(x + b) = x^2 + x(a + b) + ab
- (x + a)^2 = (x + a)(x + a) = x^2 + 2ax + a^2
This upcoming week my schedule looks wide open so I shouldn’t have any excuses not to get some serious work done. I HATE setting a goal for myself and not achieving it and still plan on getting through the course Algebraic Basics by the end of Week 8. To do so, I’ll need to finish off the second half of Quadratics and Polynomials, get through Equations and Geometry and then complete the course challenge all by next Sunday. I will not be happy if I find myself starting Week 8’s post the same way I started this one…