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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.

(6x^(5)-2x^(4)-1)/(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.\newline6x52x41x= \frac{6 x^{5}-2 x^{4}-1}{x}=

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.\newline6x52x41x= \frac{6 x^{5}-2 x^{4}-1}{x}=
  1. Divide first term: To divide a polynomial by a monomial, we divide each term of the polynomial by the monomial. We start with the first term of the polynomial 6x56x^5.\newlineDividing 6x56x^5 by xx gives us 6x46x^4.
  2. Divide second term: Next, we divide the second term of the polynomial 2x4-2x^4 by xx.\newlineDividing 2x4-2x^4 by xx gives us 2x3-2x^3.
  3. Divide constant term: The last term of the polynomial is a constant term 1-1, which does not contain the variable xx. When we divide a constant by xx, we cannot simplify it further, so it becomes the remainder of the division.\newlineDividing 1-1 by xx gives us 1/x-1/x, which we write as the remainder.
  4. Combine divided terms: Combining all the terms we have divided, we get the polynomial part p(x)=6x42x3p(x) = 6x^4 - 2x^3 and the remainder 1/x-1/x.\newlineSo, the division can be expressed as p(x)+kxp(x) + \frac{k}{x}, where p(x)=6x42x3p(x) = 6x^4 - 2x^3 and k=1k = -1.