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Okay. So I am in this special program where you work at your own pace. We have four teachers (english, math, science, and social studies), but my math teacher will not help me. He is supposed to, but he would rather help people who have already passed the class they are supposed to be in and have basically skipped a grade of math and gone on to the next than help the people who may just possibly fail because they aren't getting help. I'm kind of afraid that I'm going to fail because, basically I have 5 weeks to do about half a year of work. Okay, so now that I have told you the reason for all the help I am going to need I'm going to write what questions I need help learning how to do... Oh and I have learned how to do most of the remaining stuff out of the book, but I am posting the ones that I'm not 100% sure about. I don't want people to do the problems for me, just to help me by giving me a way to solve it.


So here is the 1st type of problem:

Use synthetic substitution to find g(3) and g(-4) for each function.

g(x)=x^3 + 2x^2 - 3x + 1


I think that you are supposed to solve it like a f(x) problem, but I'm not sure.




2nd type of problem:

Given a ploynomial and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials.

x^3 - x^2 - 10x - 8; x +1


I have absolutely no clue how do these either.


That is all I need help with for now. I greatly appriciate the help anyone gives me. By the way, the chapter of the book that these problems are in is called The Remainder and Factor Theorems. That is just incase you need to know what this is supposed to be about.

Yeah. f, g, h etc. are just letters to name the different functions. When you see SOMETHING(STUFF), you plug that STUFF into the function of SOMETHING.
So you're given that when you plug x into the function, x^3 + 2x^2 - 3x + 1 spits out. For example, when you plug a p into the function, a p should show up wherever there's an x:
g(p) = (p)^3 + 2(p)^2 - 3(p) + 1

So with your question, plug a 3 in and get:
g(3) = (3)^3 + 2(3)^2 - 3(3) + 1

Then you simplify the right side.

Later (like probably the next section of the book), you'll be doing stuff like g(h(x)). In that case, just use h(x) as the STUFF and you should be fine.





You'll need to use polynomial division or synthetic division, whichever is easier for you. Synthetic is faster if you're good at it. If you need a refresher, both can be found in this Wikipedia article.

After you get the resulting quadratic equation (there should be no remainder if you did it right,) whip out the good old quadratic formula, or just factor it by hand if it's something ridiculously easy.

Any clarification needed?

That's why I left a link, lol.