Question

divide polynomials by x (no remainders)
divide the polynomials.
your answer should be a polynomial.
\\(\frac{x^4 + 5x^3 + 3x^2}{x}\\) =

Explanation:

Step1: Divide each term by \( x \)

For the first term \( \frac{x^4}{x} \), using the rule \( \frac{x^m}{x^n}=x^{m - n} \) (here \( m = 4 \), \( n = 1 \)), we get \( x^{4-1}=x^3 \).
For the second term \( \frac{5x^3}{x} \), with \( m = 3 \), \( n = 1 \), we have \( 5x^{3 - 1}=5x^2 \).
For the third term \( \frac{3x^2}{x} \), with \( m = 2 \), \( n = 1 \), we get \( 3x^{2 - 1}=3x \).

Step2: Combine the terms

Combine the results from each division: \( x^3+5x^2 + 3x \).

Answer:

\( x^3 + 5x^2 + 3x \)