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Advanced Algebra

I hope you all had a very nice weekend. Now, it is back to math :) Here are the answers from the previous post on Beginning Algebra.

(x + 3)(x + 7)

There is a common factor involved. x^{3} - 18x^{2} - 40 x = x(x^{2} - 18x - 40) Now to find the two numbers that multiply to -40 and add to -18. They are -20 and +2. So the original equation factors into x(x - 20)(x + 2).

The first step in solving a quadratic equation by factoring is to put everything on one side of the equation. this has already been done. To factor the original equation we get (x + 3)(x + 8) = 0. Now if two numbers multiply to zero, then one of them has to be zero. so x + 3 = 0 OR x + 8 = 0. Then x = -3 OR x = -8.

I'm never quite sure which book comes next since I've seen it done both ways. Is it Advanced Algebra or Geometry????? For this post I am going to talk about the Advanced Algebra book next because that is the one I picked up (although that is the order that we've done them in.)

The Advanced Algebra book also comes with a Home Companion book that lays out the entire main book into a daily lesson plan format. This book has 10 chapters and is divided into 101 daily lessons which cover some pretty intense Algebra. Things like: radicals, logarithms, graphing, systems of equations, more factoring, linear programming, sequences, permutations and much more.

The book ends with a section entitled, "The Hardest Problem in Advanced Algebra". It also has "Looking Back" chapters that take some time to go back and revisit topics from Beginning Algebra. The chapters are numbered as 1/2 chapters, so I guess that, technically speaking, there are more than 10 chapters.

Due to my limited knowledge of how to code things properly, I am somewhat limited to the types of problems I can put up here since many of them involve square roots and graphs and complex fractions and I'm not sure how to get those to look the right way. I have, however, found a few function problems which do not require anything too complex, so here goes:

Let function f by given by the rule f(x) = 2x + 7. The domain and co-domain are the real numbers. What would f(3) equal?

What is the equation of the circle whose center is (5, 88) and whose radius is 12?