Divide the polynomials. Your answer should be in the form p(x)+(k)/(x) where p is a polynomial and k is an integer. (4x^(3)-3x+1)/(x)=

Divide by x individually: Divide each term of the polynomial by x individually. Divide 4x^3 by x, -3x by x, and 1 by x. 4x^3 / x = 4x^2 -3x / x = -3 1 / x remains as it is because 1 is not divisible by x.Combine the division results: Combine the results of the division. The polynomial part p(x) is the combination of the terms that were divided without a remainder. p(x) = 4x^2 - 3 The remainder is the term that could not be divided evenly by x, which is 1/x.Write the final answer: Write the final answer in the form p(x) + (k)/(x). The polynomial part is 4x^2 - 3, and the remainder is 1/x. So, the final answer is 4x^2 - 3 + (1)/(x).

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Math Problems

Algebra 1

Powers with decimal and fractional bases

Full solution

Q. Divide the polynomials.

\newline

Your answer should be in the form

p(x)+\frac{k}{x}

where

p

is a polynomial and

k

is an integer.

\newline

\frac{4 x^{3}-3 x+1}{x}=

Divide by x individually: Divide each term of the polynomial by x individually. $\newline$ Divide $4x^3$ by $x$ , $-3x$ by $x$ , and $1$ by $x$ . $\newline$ $\frac{4x^3}{x} = 4x^2$ $\newline$ $\frac{-3x}{x} = -3$ $\newline$ $\frac{1}{x}$ remains as it is because $1$ is not divisible by $x$ .
Combine the division results: Combine the results of the division. $\newline$ The polynomial part $p(x)$ is the combination of the terms that were divided without a remainder. $\newline$ $p(x) = 4x^2 - 3 (\newline$ )The remainder is the term that could not be divided evenly by \$ x \), which is $ \frac{1}{x} $.
Write the final answer: Write the final answer in the form $p(x) + \frac{k}{x}$.$\newline$The polynomial part is $4x^2 - 3$, and the remainder is $\frac{1}{x}$.$\newline$So, the final answer is $4x^2 - 3 + \frac{1}{x}$.