Dividing Polynomials...Hooray!

As a home educating mother, it is crucial that I understand how to do algebra and higher math so that I can help my children if they need it. I haven't had algebra since the ninth grade and that is as far as I went (well, Geometry but I sucked at the time). Anyhow, we've been using Ray's Arithmetic for my son, he wanted to go straight to algebra and so following his lead, we did. We were flying right along until we hit division of polynomials by polynomials. The directions in this classic math program are a bit hard to comprehend at times.

I was troubled because I couldn't "get it"; my son couldn't either. After a few days I gave up, ready to purchase another algebra curriculum; however, I woke up this past Saturday morning with a clear head and thought to myself, "I can do those problems." First I went and reviewed algebra for addition, subtraction, and multiplication...that was all it took. I knew these rules below already but was so intimidated by this type of division that I had a brain fart. I had forgotten that when you get ready to subtract, you MUST change the signs to the opposite. For instance, if my product (the answer to my multiplication portion) has + and/or - before any letter (with or without exponents), I need to change those signs when I go to subtract, i.e if my product was +7a5-6a2x, I need to change it to -7a5+6a2x and then subtract. Also worth noting are the basics: When multiplying a opposite signs, i.e +/- the product is negative, when multiplying two negatives; the product is a positive, when multiplying two positives; the product is positive. The same for rules apply for dividing. I had to also remember to SUBTRACT the exponents when dividing and ADD exponents when multiplying.

When dividing polynomials, you divide the first term in the dividend, by the first term of the divisor. After you achieve your partial quotient, you multiply that by the entire polynomial divisor. Line up letters and exponents that match and subtract. If *zero* hasn't been achieved you then bring down any remainders (I like to bring down all leftover terms from the original dividend so that I keep everything straight) and divide only the first term in the difference of the dividend brought down. You keep going until you reach Zero.

That said, I wanted to show my work for the following problem:

Divide a5-5a4x+10a3x2-10a2x3+5ax4-x5 by a2-2ax+x2



I did like 15 problems after figuring out how to do these and now I am able to help my son. It feels really good to know that although I'm 37, I'm capable of being self-taught on math that I thought I'd never have to remember (formula wise, we technically use algebra all the time, we just don't know the specific terms and formulas). :-)