By Dawkins P.
Listed below are my on-line notes for my Algebra path that I educate the following at Lamar college, even though i need to admit that it has been years on the grounds that I final taught this direction. At this aspect in my occupation I quite often educate Calculus and Differential Equations.Despite the truth that those are my "class notes" they need to be obtainable to an individual eager to research Algebra or desiring a refresher for algebra. i have attempted to make the notes as self contained as attainable and don't reference any ebook. even though, they do think that you've got has a few publicity to the fundamentals of algebra at some point soon ahead of this. whereas there's a few assessment of exponents, factoring and graphing it really is assumed that no longer loads of assessment can be had to remind you ways those issues work.Here are a few warnings to my scholars who could be the following to get a duplicate of what occurred on an afternoon that you simply overlooked.
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Additional info for College Algebra (2007)(en)(350s)
4x 2 − x ) ( 6 − 3x ) = 24 x 2 − 12 x 3 − 6 x + 3 x 2 = −12 x 3 + 27 x 2 − 6 x [Return to Problems] (d) ( 3 x + 7 y )( x − 2 y ) We can still FOIL binomials that involve more than one variable so don’t get excited about these kinds of problems when they arise. aspx College Algebra ( ) (e) ( 2 x + 3) x 2 − x + 1 In this case the FOIL method won’t work since the second polynomial isn’t a binomial. Recall however that the FOIL acronym was just a way to remember that we multiply every term in the second polynomial by every term in the first polynomial.
Aspx College Algebra Do not make the following factoring mistake! a 2 + b2 ≠ ( a + b ) 2 This just simply isn’t true, so be careful not to make this very common mistake. The sum of two perfect squares doesn’t factor! Factoring Polynomials with Degree Greater than 2 There is no one method for doing these in general. However, there are some that we can do so let’s take a look at a couple of examples. Example 5 Factor each of the following. (a) 3 x 4 − 3 x3 − 36 x 2 [Solution] (b) x 4 − 25 [Solution] (c) x 4 + x 2 − 20 [Solution] Solution (a) 3 x 4 − 3 x3 − 36 x 2 In this case let’s notice that we can factor out a common factor of 3x2 from all the terms so let’s do that first.
So, the x-3 above could cancel since it multiplied the whole numerator and the whole denominator. However, the x’s in the reduced form can’t cancel since the x in the numerator is not times the whole numerator. To see why the x’s don’t cancel in the reduced form above put a number in and see what happens. Let’s plug in x=4. aspx College Algebra 4 −1 3 = 4 4 4 −1 = −1 4 Clearly the two aren’t the same number! So, be careful with canceling. As a general rule of thumb remember that you can’t cancel something if it’s got a “+” or a “-” on one side of it.
College Algebra (2007)(en)(350s) by Dawkins P.