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Divide the polynomials.
Your answer should be a polynomial.

(2x^(4)+4x^(3)-x^(2))/(x)=

Divide the polynomials.\newlineYour answer should be a polynomial.\newline2x4+4x3x2x= \frac{2 x^{4}+4 x^{3}-x^{2}}{x}=

Full solution

Q. Divide the polynomials.\newlineYour answer should be a polynomial.\newline2x4+4x3x2x= \frac{2 x^{4}+4 x^{3}-x^{2}}{x}=
  1. Understand Polynomial Division: Understand the division of polynomials. When dividing a polynomial by a monomial, you divide each term of the polynomial by the monomial.
  2. Divide First Term by x: Divide the first term of the polynomial by xx.\newline2x4x=2x3 \frac{2x^4}{x} = 2x^3 \newlineCheck for math errors by multiplying back: 2x3x=2x42x^3 \cdot x = 2x^4, which matches the original term.
  3. Divide Second Term by x: Divide the second term of the polynomial by xx.\newline4x3x=4x2 \frac{4x^3}{x} = 4x^2 \newlineCheck for math errors by multiplying back: 4x2x=4x34x^2 \cdot x = 4x^3, which matches the original term.
  4. Divide Third Term by x: Divide the third term of the polynomial by xx.\newlinex2x=x \frac{-x^2}{x} = -x \newlineCheck for math errors by multiplying back: xx=x2-x \cdot x = -x^2, which matches the original term.
  5. Combine Division Results: Combine the results of the divisions to get the final answer.\newlineThe result of dividing the polynomial 2x4+4x3x22x^4 + 4x^3 - x^2 by xx is 2x3+4x2x2x^3 + 4x^2 - x.