Question

find the quotient and remainder using synthetic division.

\frac{x^4 + 6x^3 - 22x + 10}{x + 3}

the quotient is

the remainder is

Explanation:

Step 1: Identify coefficients and divisor

Write the dividend with all powers of \(x\): \(x^4 + 6x^3 + 0x^2 - 22x + 10\). The coefficients are \(1, 6, 0, -22, 10\), and the divisor \(x + 3\) gives \(c = -3\).

Step 2: Perform synthetic division

Set up the synthetic division:

$$
LATEXBLOCK0
$$

Step 3: Write quotient and remainder

The bottom row coefficients \(1, 3, -9, 5\) represent the quotient \(x^3 + 3x^2 - 9x + 5\), and the last value \(-5\) is the remainder.

Answer:

The quotient is \(x^3 + 3x^2 - 9x + 5\)
The remainder is \(-5\)