Question

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

\\((15x^2 + 14x - 6) \div (5x - 2)\\)

\\((15x^2 + 14x - 6) \div (5x - 2) = \square + \frac{\square}{5x - 2}\\)

(simplify your answers. do not factor.)

Explanation:

Set up the division

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK0
$$

Divide the leading terms

Using the Polynomial Long Division knowledge point

$$ \frac{15x^2}{5x} = 3x $$

Multiply and subtract the first term

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK1
$$

Divide the remaining terms

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK2
$$

Write in division algorithm form

Using the Division Algorithm knowledge point

$$
LATEXBLOCK3
$$

Answer:

\((15x^2 + 14x - 6) \div (5x - 2) =\) <blank>\(3x + 4\)</blank> \(+\frac{\text{}2\text{}}{5x - 2}\)