Question

Divide the polynomials.

Answer 1

`\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{(x^(5)+(3* x^(2)) +(2* x) )/(x)} \end{gathered}$}`

Takes into account expressions that have not yet been taken into account.

`\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{\red{\\ot{x}}(x-1)(x^(3)+x^(2) +x-2) }{\red{\\ot{x}} } } \end{gathered}$}`

Cancel x in both the numerator and the denominator.

`\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{(x-1)(x^(3)+x^(2) +x-2) } \end{gathered}$}`

The expression expands

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x^(4)-3x+2 } \end{gathered}$} }`

Answer 2

x^4-3x+2

Explanation:

There are several different ways to divide algebraic expressions. Here the most simple way to do it (and good idea to try first) is to FACTOR and CANCEL.

see image.

Factor an x from the top. Cancel that x with the bottom x. See image.

(***Also, note: never "cancel" anything connected by a + or a - )