Question

What is the quotient of $\frac{3x^3+4x+11}{x^2-3x+2}$

• A. $25x-7+\frac{3x+9}{x^2-3x+2}$
• B. $3x+9+\frac{25x-7}{x^2-3x+2}$
• C. $25x-7$
• D. $3x+9$

Answer 1

The correct option is D $3x+9$

Step 1: $$\begin{array}{c}{x}^2-3x+23x^3+0x^2+4x+11\end{array}$$

Step 2, 3, 4:
$$\begin{array}{c}3x\\ x^2-3x+23x^3+0x^2+4x+11\\ \underset{–}{3x^3-9x^2+6x-+-}2\\ 9x^2-2x+11\end{array}$$

Step 5, 6, 7:
$$\begin{array}{c}3x+9\\ x^2-3x+23x^3+0x^2+4x+11\\ \underset{–}{3x^3-9x^2+6x-+-}2\\ 9x^2-2x+11\\ \underset{–}{9x^2-27x+18-+-}\\ 25x-7\end{array}$$
Step 8: $3x+9+\frac{25x-7}{x^2-3x+2}$

Quotient = $3x+9$