Question

Divide using either synthetic division or long division.
(3x^3 + 4x^2 - x + 7) / (x + 2)

Answer 1

Quotient = 3x² - 2x + 3

Remainder = 1

Explanation:

We have to solve:
`(3 x^(3) + 4 x^(2) - x + 7)/(x + 2)`

We will use synthetic division to calculate this divisor

First, take the constant term of the divisor with the opposite sign and write it to the left. Write the coefficients of the dividend expression to the right Where there is no coefficient for a specific x term, use 0

Step 1: Write down the first coefficient asis

| x³ x² x¹ x⁰
2 | 3 4 -1 7 ← Coefficient row
|
---------------------------------

3 ← Result Row

Step 2: Multiply the entry in the left part of the table by the last entry in the result row and add he obtained result to the next coefficient of the dividend, and write down the sum.

| x³ x² x¹ x⁰
-2 | 3 4 -1 7
| -6 -6 = -2 x 3
---------------------------------

3 -2 -2 = 4 + (-6)

Repeat step 2 until we have finished with all the entries. These are the snapshots of each computation. Current operands are in bold

| x³ x² x¹ x⁰
-2 | 3 4 -1 7
| -6 4
---------------------------------

3 -2 3

| x³ x² x¹ x⁰
-2 | 3 4 -1 7
| -6 4 -6
---------------------------------

3 -2 3 1

The last entry in the result table shows the remainder of the division

The resultant coefficients are 3, -2, 3, 1

Therefore the answer is
Quotient = 3x² - 2x + 3
Remainder = 1