Question

question 3 of 6
enter the correct answer in the box.
use long division to determine the quotient of the following expression.
$(45x^2 + 2x - 112) \div (5x + 8)$
write the quotient in standard form with the term of largest degree on the left.

Explanation:

Step1: Divide the leading terms

Divide the leading term of the dividend \(45x^2\) by the leading term of the divisor \(5x\). So, \(\frac{45x^2}{5x} = 9x\).

Step2: Multiply and subtract

Multiply the divisor \((5x + 8)\) by \(9x\) to get \(45x^2 + 72x\). Now subtract this from the dividend:
\[

$$\begin{align*} (45x^2 + 2x - 112) - (45x^2 + 72x) &= 45x^2 + 2x - 112 - 45x^2 - 72x\\ &= -70x - 112 \end{align*}$$

\]

Step3: Divide the new leading terms

Divide the leading term of the new dividend \(-70x\) by the leading term of the divisor \(5x\). So, \(\frac{-70x}{5x} = -14\).

Step4: Multiply and subtract again

Multiply the divisor \((5x + 8)\) by \(-14\) to get \(-70x - 112\). Subtract this from the new dividend:
\[
(-70x - 112) - (-70x - 112) = 0
\]
Since there is no remainder, the quotient is the sum of the terms we found in Step1 and Step3.

Answer:

\(9x - 14\)