By Dawkins P.
Listed below are my on-line notes for my Algebra direction that I train right here at Lamar collage, even supposing i need to admit that it has been years due to the fact I final taught this path. At this aspect in my profession I typically educate Calculus and Differential Equations.Despite the truth that those are my "class notes" they need to be available to an individual desirous to study Algebra or desiring a refresher for algebra. i have attempted to make the notes as self contained as attainable and don't reference any booklet. besides the fact that, they do imagine that you have has a few publicity to the fundamentals of algebra sooner or later ahead of this. whereas there's a few evaluate of exponents, factoring and graphing it truly is assumed that no longer loads of evaluate should be had to remind you the way those subject matters work.Here are a few warnings to my scholars who might be right here to get a duplicate of what occurred on an afternoon that you simply ignored.
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Sample text
Next, let’s take a quick look at polynomials in two variables. Polynomials in two variables are algebraic expressions consisting of terms in the form ax n y m . The degree of each term in a polynomial in two variables is the sum of the exponents in each term and the degree of the polynomial is the largest such sum. Here are some examples of polynomials in two variables and their degrees. x 2 y − 6 x 3 y12 + 10 x 2 − 7 y + 1 degree : 15 6 x 4 + 8 y 4 − xy 2 degree : 4 x 4 y 2 − x3 y 3 − xy + x 4 degree : 6 6 x − 10 y + 3 x − 11 y degree : 14 14 3 In these kinds of polynomials not every term needs to have both x’s and y’s in them, in fact as we see in the last example they don’t need to have any terms that contain both x’s and y’s.
Next, we recalled that we change the order of a multiplication if we need to so we flipped the x and the “-1”. Finally, we dropped the “-1” and just went back to a negative sign in the front. Typically when we factor out minus signs we skip all the intermediate steps and go straight to the final step. Let’s now get back to the problem. The rational expression becomes, x 2 − 25 ( x − 5 )( x + 5 ) = 5x − x2 − x ( x − 5) At this point we can see that we do have a common factor and so we can cancel the x-5.
Let’s remember how do to do this with a quick number example. 5 3 − 6 4 In this case we need a common denominator and recall that it’s usually best to use the least common denominator, often denoted lcd. In this case the least common denominator is 12. So we need to get the denominators of these two fractions to a 12. This is easy to do. In the first case we need to multiply the denominator by 2 to get 12 so we will multiply the numerator and denominator of the first fraction by 2. aspx College Algebra this is equivalent to multiplying the fraction by 1 since a = 1 .