Q. Divide the polynomials. Your answer should be in the form p(x)+xk where p is a polynomial and k is an integer.x6x5−2x4−1=
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 6x5.Dividing 6x5 by x gives us 6x4.
Divide second term: Next, we divide the second term of the polynomial −2x4 by x.Dividing −2x4 by x gives us −2x3.
Divide constant term: The last term of the polynomial is a constant term −1, which does not contain the variable x. When we divide a constant by x, we cannot simplify it further, so it becomes the remainder of the division.Dividing −1 by x gives us −1/x, which we write as the remainder.
Combine divided terms: Combining all the terms we have divided, we get the polynomial part p(x)=6x4−2x3 and the remainder −1/x.So, the division can be expressed as p(x)+xk, where p(x)=6x4−2x3 and k=−1.
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