Question

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

\frac{4x^4 - 4x^2 + 6x}{x - 2}

\frac{4x^4 - 4x^2 + 6x}{x - 2} = 4x^3 8x^2 + 12x + 30 + \frac{60}{x - 2}
(simplify your answers. do not factor. use integers or fractions for any numbers in the expressions.)

Explanation:

Set up the division with placeholders

Using the Polynomial Long Division knowledge point

$$ \frac{4x^4 + 0x^3 - 4x^2 + 6x + 0}{x - 2} $$

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 linear term

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK2
$$

Divide the constant term

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK3
$$

Answer:

\(\frac{4x^4 - 4x^2 + 6x}{x - 2} =\) <blank>\(4x^3 + 8x^2 + 12x + 30\)</blank> \(+\frac{\text{}60\text{}}{x - 2}\)