Question

divide.

\\((x^3 + 6x^2 + 9x + 4) \div (x + 1)\\)

\\((x^3 + 6x^2 + 9x + 4) \div (x + 1) = \box + \frac{\box}{x + 1}\\)

(simplify your answers. do not factor.)

Explanation:

Set up the division

$$ \frac{x^3 + 6x^2 + 9x + 4}{x + 1} $$

Perform synthetic division

Using root \(x = -1\):

$$
LATEXBLOCK0
$$

Write the quotient and remainder

$$ \text{Quotient} = x^2 + 5x + 4,\quad \text{Remainder} = 0 $$

Answer:

Divide.

$$(x^3+6x^2+9x+4) \div (x+1)$$

$$(x^3+6x^2+9x+4) \div (x+1) =$$

<blank>\(x^2+5x+4\)</blank> \(+\frac{\text{0}}{x+1}\)
(Simplify your answers. Do not factor.)