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Divide the polynomials. Your answer should be in the form 
p(x)+(k)/(x) where 
p is a polynomial and 
k is an integer.

(3x^(2)-10)/(x)=◻

Divide the polynomials. Your answer should be in the form p(x)+kx p(x)+\frac{k}{x} where p p is a polynomial and k k is an integer.\newline3x210x= \frac{3 x^{2}-10}{x}=\square

Full solution

Q. Divide the polynomials. Your answer should be in the form p(x)+kx p(x)+\frac{k}{x} where p p is a polynomial and k k is an integer.\newline3x210x= \frac{3 x^{2}-10}{x}=\square
  1. Identify dividend and divisor: Identify the dividend and the divisor.\newlineIn the expression (3x210)/x(3x^2 - 10) / x, 3x2103x^2 - 10 is the dividend and xx is the divisor.\newlineDividend: 3x2103x^2 - 10\newlineDivisor: xx
  2. Perform division of first term: Perform the division of the first term of the dividend by the divisor.\newlineDivide 3x23x^2 by xx to get 3x3x.\newlineCalculation: 3x2x=3x\frac{3x^2}{x} = 3x
  3. Perform division of second term: Perform the division of the second term of the dividend by the divisor.\newlineSince 10-10 does not contain the variable xx, it cannot be divided by xx in the same way as the first term. Instead, it will be represented as a fraction with xx in the denominator.\newlineCalculation: 10/x=10x-10 / x = -\frac{10}{x}
  4. Combine division results: Combine the results of the divisions to express the answer in the form p(x)+kx p(x) + \frac{k}{x} .\newlineThe polynomial part p(x) p(x) is the result of the division of the terms containing x x , and k k is the integer resulting from the division of the constant term.\newlineCalculation: 3x2x10x=3x10x \frac{3x^2}{x} - \frac{10}{x} = 3x - \frac{10}{x}