Question

use synthetic division to divide.\\(
\frac{7x^2 - 5}{x - 3}\\)\\(
\frac{7x^2 - 5}{x - 3} = \square\\)

Explanation:

Step1: Identify root & coefficients

Root of divisor $x-3$ is $3$.
Coefficients of dividend $7x^2+0x-5$: $7, 0, -5$

Step2: Bring down leading coefficient

$$\begin{array}{r|rrr} 3 & 7 & 0 & -5 \\ \hline & & & \\ \hline & 7 & & \end{array}$$

Step3: Multiply & add to next coefficient

$7 \times 3 = 21$; $0 + 21 = 21$

$$\begin{array}{r|rrr} 3 & 7 & 0 & -5 \\ \hline & & 21 & \\ \hline & 7 & 21 & \end{array}$$

Step4: Multiply & add to last coefficient

$21 \times 3 = 63$; $-5 + 63 = 58$

$$\begin{array}{r|rrr} 3 & 7 & 0 & -5 \\ \hline & & 21 & 63 \\ \hline & 7 & 21 & 58 \end{array}$$

Step5: Write quotient & remainder

Quotient: $7x + 21$, Remainder: $58$

Answer:

$7x + 21 + \frac{58}{x-3}$