Polynomials: need the basics; also for equations

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msbionik

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Jun 11, 2006
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Hi I'm new to the board. I just recently went back to school and I cannot remember anything I learned in high school--it's been about 15 years! I am in Algebra class and the teacher is foreign-- I cannot understand a word she says and when I do understand what she says, I just cannot comprehend the whole math thing.

Can anyone out there help me get the basics down on polynomials and other types of equations?

I would appreciate any help.

Thanks!
:?
 
Can anyone out there help me get the basics down on polynomials and other types of equations?
Click to expand...

Polynomials are equations likeP(x)= x^4+ 4x^3+ 7x^2 + 2x + 10.

And to do synthetic division with a polynomial is if

it says can x^4+ 4x^3+ 7x^2 + 2x + 10 be divided into (x+3) evenly, you do:
-3| 1 4 7 2 10
0 -3 -3 -12 -30
1 1 4 -10 |-20

What you do is you Add the top line with the middle line to get the bottom line. And you use the bottom line to multiply with-3 so that you get the next blank number on teh middle line.

And when they say divide into (x+3), when you do synthetic division, the + or - sign is always the opposite. Hence the -3 in my equation.

---
I don't really know what you need help on, so I'm just giving this first...
 
We cannot teach lessons here, and in order to provide links, I'm afraid you're going to need to be much more specific.

"Polynomials" could mean "combining like terms", "adding and subtracting", "multiplying", "doing long division", "doing synthetic division", "graphing", "determining end behavior", "factoring", "solving", or other things.

"Equations" could mean "linear", "radical", "quadratic", "general polynomial", "absolute value", "rational", or other things, and you might be referring to graphing or solving. Or you might mean "inequalities".

Please state specifically the topics for which you are seeking links to lessons. Thank you.

Eliz.
 
Sorry for not being specific...

For instance, it is actually dividing polynomials that I do not understand.

Here is the problem: -3x+4/x+2.

WHat do I do first? And how do I do it?
 
What you have posted means the following:

. . . . .\(\displaystyle \L -3x\,+\,\frac{4}{x}\,+\,2\)

Is that what you meant? If so, there is nothing to divide.

If not, did you mean something more like (-3x + 4)/(x + 2), which may alse be written as the following?

. . . . .\(\displaystyle \L \frac{-3x\,+\,4}{x\,+\,2}\)

In either case, what is the exact wording of the instructions? Are you supposed to "simplify"? Or have you recently studied polynomial long division, and you're supposed to apply that technique?

Thank you.

Eliz.

Polynomial Long Division
 
msbionik said:
It is long division polynomials
Click to expand...
Then the link (above) should be helpful, as should the following:

. . . . .Paul's Online Notes: Dividing Polynomials

. . . . .MathCentral: How Do We Divide Polynomials?

. . . . .WTAMU: Division of Polynomials

. . . . .Univ. of N Texas: Long Division of Polynomials

. . . . .Wikipedia: Polynomial Long Division

(We can't teach generalized lessons here, is why I'm providing the links. Once you have learned the general techniques, you can attempt the exercise. If you get stuck, we can then provide specific assistance.)

I hope that helps a bit. :D

Eliz.
 
Thank you so much for everything, Stapel. It just gets frustrating but I'm sure I'll get it.
 
msbionik said:
How do I know when there is a "missing term" when dividing polynomials?
Click to expand...
Look at the powers. If there is a steady decline from whatever is the highest-degree term, down through x<sup>2</sup>, x, and then a constant, then there are no missing terms. But if there is a jump, say from x<sup>4</sup> to x<sup>2</sup>, then there is a missing term.

Eliz.
 
Thank you so much Eliz. I think I am getting the hang of it... I appreciate your time.
 
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