this post will cover just some of the basics of polynomial functions. This post will focus on the divisioin of polynomials through long division and Factor Theorum.
Using Long Divison:
As many of you should alrady know how to divide, dividing with exponents isn't that much harder. So lets start with this example first. Use long division to divide 36x^3 - 6x^2 + 3x - 33 by 3x + 1 (Note: BY 3x + 1 is what they want you to divide with). So how do we do it?
1. Write down the question first
2. Like you would do for normal divison, ask yourself how many times can 3x go into 36x^3? (Answer: 12x^2)
3. After finding that out, treat the answer you found in #2 like 12x^2(3x + 1) in order to progress.
4. Subtract the answer.
5. Bring down the 3x from the question.
6. Repeat the same processas you did for 2. (how many times does 3x go into -18x^2? Answer: -6x)
7. Repeat steps 3, 4, 5, 6.
8. Once you have reached the remainder (-30R), you can now write down the division statement (Dividend) = (Divisor)(Quotient) + Remainder
The next thing we'll look at is how to use factor theorum to solve for a polynomial (FYI: MUCH fast and WAY easier).
If you are given a question such as: Factor x^4 + 4x^3 - x^2 - 16x - 12
So how do you do it?
1. To find the first zero, find a number for x which can cause the polynomial to equal to zero (in this case -2)
2. Your new polynomial should look like (x+2)(x^3 + 2x^2 - 5x - 6) But your not done yet.
3. Repeat step one, your zero's should now become more clear. (x + 2) (x + 3) (x^2 - x - 2)
4. Finally, factor out x^2 - x - 2 (product/sum)
Well, that's about all you need to know about long division of polynomials and factor theorum. Hope this helped.