Polynomials Problem:

1. List three factors of g(x) of the form x−r: x + 1, x - 1, x - 2
2. The smallest possible value for the degree of g is 3.
3. A function of the form axn that approximates g(x) for large values of |x| is f(x)= 3x^3.
4. This tells us that the degree of g is 3 and the coefficient of the highest degree term of g(x) is 3.
5. Use the results of your investigation above to determine a formula for the function g:
g(x)= ______________ ?

Please help me figure out the 5th question. Thanks in advance!!

The question shown above is very similar to your previous question:

http://www.jiskha.com/display.cgi?id=1265585894

In fact, this question would be a good test of your understanding.

Do try to come up with an answer, and if the computer software does not accept it, then post your answer for discussion. I am quite sure you would get the correct answer the first time.

To determine the formula for the function g(x), we can use the information given in the previous parts of the problem.

From part 1, we know that g(x) has three factors of the form x - r: (x + 1), (x - 1), and (x - 2). This means that if we were to multiply these factors together, we would get the expanded form of g(x).

(x + 1)(x - 1)(x - 2)

Expanding this expression, we can apply the distributive property to each term:

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

From part 4, we know that the highest degree term of g(x) has a coefficient of 3. Therefore, we can multiply the entire expression by 3 to get the correct coefficient:

3(x^3 - 2x^2 - x + 2)
= 3x^3 - 6x^2 - 3x + 6

So, the formula for the function g(x) is:

g(x) = 3x^3 - 6x^2 - 3x + 6