Use the long division method to find the result when

Question

3x^3 + 5x^2 + 20x 12 is divided by 3x + 2

Answer 1

To divide 3x^3 + 5x^2 + 20x + 12 by 3x + 2 using long division, follow these steps:

Step 1: Write the dividend (3x^3 + 5x^2 + 20x + 12) and divisor (3x + 2).

___________
3x + 2 ) 3x^3 + 5x^2 + 20x + 12

Step 2: Divide the first term of the dividend (3x^3) by the first term of the divisor (3x), which gives x^2. Place this result above the horizontal line.

x^2
___________
3x + 2 ) 3x^3 + 5x^2 + 20x + 12

Step 3: Multiply the divisor (3x + 2) by the result (x^2) and write the result below the dividend, keeping the terms in alignment.

x^2
___________
3x + 2 ) 3x^3 + 5x^2 + 20x + 12
- (3x^3 + 2x^2)

x^2
___________
3x + 2 ) 3x^3 + 5x^2 + 20x + 12
- (3x^3 + 2x^2)
__________
3x^2 + 20x + 12

Step 4: Repeat steps 2 and 3 with the new dividend (3x^2 + 20x + 12).

x^2 + 7x
___________
3x + 2 ) 3x^3 + 5x^2 + 20x + 12
- (3x^3 + 2x^2)
__________
3x^2 + 20x + 12
- (3x^2 + 2x)

x^2 + 7x
___________
3x + 2 ) 3x^3 + 5x^2 + 20x + 12
- (3x^3 + 2x^2)
__________
3x^2 + 20x + 12
- (3x^2 + 2x)
_____________
18x + 12

Step 5: Repeat steps 2 and 3 with the new dividend (18x + 12).

x^2 + 7x + 6
_______________
3x + 2 ) 3x^3 + 5x^2 + 20x + 12
- (3x^3 + 2x^2)
__________
3x^2 + 20x + 12
- (3x^2 + 2x)
_____________
18x + 12
- (18x + 12)
_______________
0

Step 6: Since the new dividend (18x + 12) has become zero, the division is completed.

Therefore, the result of dividing 3x^3 + 5x^2 + 20x + 12 by 3x + 2 is x^2 + 7x + 6.