# polynomial division

1. ### B Questions regarding polynomial divisions and their roots

Hello everyone, Going through calculus study, there is a vague point regarding polynomials I'd like to make clear. Say there's a polynomial $f$ with a root at $a$ with multiplicity $2$, i.e. $f(x)=(x-a)^2g(x)$ where $g$ is some other polynomial. I define $h(x)=\frac {f(x)} {x-a}$...
2. ### Factoring Combinatorial Functions

Homework Statement Define {x \choose n}=\frac{x(x-1)(x-2)...(x-n+1)}{n!} for positive integer n. For what values of positive integers n and m is g(x)={{{x+1} \choose n} \choose {m}}-{{{x} \choose n} \choose {m}} a factor of f(x)={{{x+1} \choose n} \choose {m}}? Homework Equations The idea...
3. ### 5 degree equation contains imaginary value?

Homework Statement Homework Equations polynomial equation $$(a+b)^2 = \sum_{k=0}^{n} \binom nk a^{n-k} b^k$$ The Attempt at a Solution i get  \frac {1} {32} + \frac {5} {16}\frac {3^{0.5}i} {2} +\frac {10} {8}\frac {3i^2} {4} + \frac {10} {4}\frac {3^{1.5}i^3} {8} + \frac {5} {2} \frac...
4. ### Dividing polynomials question

Mod note: Moved from a technical math section, so missing the template. I have this question and the answer but my mathXL does not show me how it came to this conclusion. (4s3+4s2 + 72)/ s+3 I got all the way to the answer 4s2 - 8s The correct answer is 4s2 - 8s + 24 I just don't know the...