Project Deadline's Tommorow! Please help me quick!

[captainbagixx]

Polynomial Functions
Factor Theorem

1. Let f(x)=2x³-ax+bx+2 and g(x)=4x³+8x²+ax+b. It is given that f(x) is divisible by x-2, and 2x+1 is a factor of g(x).
a.) Find the values of a and b.
b.) Determine whether 3x-1 is a factor of 2f(x)-g(x).

2. Let f(x)=px³-6x²+3x+2q and h(x)=x³-5x²-px+q. It is given that x+2 is a common factor of f(x) and h(x).
a.) Find the values of p and q.
b.) Hence, solve f(x)=h(x).

I need quick answers cause I'm submitting this one tomorrow. Please help me.. My friend and I have been trying to solve this one to no avail. We messed up and lose hope. Please help!

 

[stapel]

Polynomial Functions
Factor Theorem

1. Let f(x)=2x³-ax+bx+2 and g(x)=4x³+8x²+ax+b. It is given that f(x) is divisible by x-2, and 2x+1 is a factor of g(x).
a.) Find the values of a and b.
b.) Determine whether 3x-1 is a factor of 2f(x)-g(x).

2. Let f(x)=px³-6x²+3x+2q and h(x)=x³-5x²-px+q. It is given that x+2 is a common factor of f(x) and h(x).
a.) Find the values of p and q.
b.) Hence, solve f(x)=h(x).

My friend and I ... need quick answers ....

If you are unable, after however long the two of you have had for this project, even to make a start, then you need much more than us cheating for you and giving you the answers (even if this were that sort of site, which it isn't -- sorry).

It is unfortunate that you two missed all those days or weeks in class when the Factor Theorem was discussed. You'll have to try replacing those missing lectures with online lessons (such as in this listing), as we cannot possibly provide that here.

Once you have studied at least two lessons from the listing, then you'll probably want to review some worked examples, such as are in this listing. After studying a few examples, you'll probably start noticing some patterns, at which point you should be prepared to at least attempt at least one part of at least one of the exercises.

(For instance, you'll probably notice a class of problem which matches the question asked in (1-a), using long polynomial division (here) to solve for variables in remainders which must, due to divisibility, equal zero. You'll note that similar reasoning and methodology can probably be applied to (2-a). And so forth.)

If you get stuck, please reply showing your efforts so far, and we'll be glad to provide hints and helps to assist in your progress. Thank you!