Question 201265
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Let *[tex \Large f(x)=a_0x^n+a_1x^{n-1}+\cdots+a_{n-1}x^1+a_nx^0] represent your polynomial.  Let *[tex \Large g(x) = bx^m] represent your monomial.


Then you are concerned with finding the quotient *[tex \Large \frac{f(x)}{g(x)}] 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{a_0x^n+a_1x^{n-1}+\cdots+a_{n-1}x^1+a_nx^0}{bx^m}]


Break it up in to separate fractions, one per term of the numerator polynomial.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{a_0x^n}{bx^m}+\frac{a_1x^{n-1}}{bx^m}+\cdots+\frac{a_{n-1}x^1}{bx^m}+\frac{a_nx^0}{bx^m}]


Then simplify each term:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{a_0}{b}x^{\small{n-m}}+\frac{a_1}{b}x^{n-1-m}+\cdots+\frac{a_{n-1}}{b}x^{1-m}+\frac{a_n}{b}x^{-m}]


Example:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{5x^5 + 6x^3 -20}{2x}]


Divide each term:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{5x^5}{2x}+\frac{6x^3}{2x}-\frac{20}{2x}]


Simplify each term:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{5}{2}x^4 + 3x^2 - \frac{10}{x}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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