Question

divide using long division. state the quotient, \\(q(x)\\), and the remainder, \\(r(x)\\).

\\(x^3 + 2x^2 - 5x + 2) \div (x - 1)\\

\\(x^3 + 2x^2 - 5x + 2) \div (x - 1) = \boxed{\quad} + \frac{\boxed{\quad}}{x - 1}\\

(simplify your answers. do not factor.)

Explanation:

Set up the division problem

Using the Polynomial Long Division knowledge point

$$ (x^3 + 2x^2 - 5x + 2) \div (x - 1) $$

Divide the leading terms

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK0
$$

Divide the next term

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK1
$$

Divide the final term

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK2
$$

Write in division algorithm form

Using the Division Algorithm knowledge point

$$
LATEXBLOCK3
$$

Answer:

Divide using long division. State the quotient, \(q(x)\), and the remainder, \(r(x)\).

$$(x^3 + 2x^2 - 5x + 2) \div (x - 1) = x^2 +$$

<blank>\(3x - 2\)</blank> \(+\frac{\text{}0\text{}}{x - 1}\)