Use the long division method to find the result when
3x^3 + 5x^2 + 20x 12 is divided by 3x + 2
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
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3x + 2 ) 3x^3 + 5x^2 + 20x + 12
- (3x^3 + 2x^2)
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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)
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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.