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

To divide the polynomial \(\frac{4x^3 - 3x + 1}{x}\), we need to divide each term in the numerator by the denominator \(x\).<br /><br />Given:<br />\[<br />\frac{4x^3 - 3x + 1}{x}<br />\]<br /><br />We can split this into separate fractions:<br />\[<br />\frac{4x^3}{x} + \frac{-3x}{x} + \frac{1}{x}<br />\]<br /><br />Now, simplify each term:<br />\[<br />\frac{4x^3}{x} = 4x^2<br />\]<br />\[<br />\frac{-3x}{x} = -3<br />\]<br />\[<br />\frac{1}{x} = \frac{1}{x}<br />\]<br /><br />Putting it all together, we get:<br />\[<br />4x^2 - 3 + \frac{1}{x}<br />\]<br /><br />So, the final answer is:<br />\[<br />4x^2 - 3 + \frac{1}{x}<br />\]