Use the long division method to find the results when
9x^3 + 24x^2 + 28x + 7 is divided by 3x + 1
To divide 9x^3 + 24x^2 + 28x + 7 by 3x + 1 using long division method, follow the steps below:
Step 1: Write the dividend (9x^3 + 24x^2 + 28x + 7) and divisor (3x + 1) in the division format:
_____________________
3x + 1 | 9x^3 + 24x^2 + 28x + 7
Step 2: Divide the first term of the dividend (9x^3) by the first term of the divisor (3x). The result will be the quotient's first term.
3x^2
Step 3: Multiply the divisor (3x + 1) by the quotient's first term (3x^2). Place the result below the dividend, aligning it with the like terms.
3x^2 + x
_____________________
3x + 1 | 9x^3 + 24x^2 + 28x + 7
- (9x^3 + 3x^2)
Step 4: Subtract the result obtained from step 3 from the corresponding term in the dividend. Write the result below the line.
3x^2 + x
_____________________
3x + 1 | 9x^3 + 24x^2 + 28x + 7
- (9x^3 + 3x^2)
-------------------
21x^2 + 28x
Step 5: Bring down the next term from the dividend (in this case, it is 28x) and continue dividing.
3x^2 + x
_____________________
3x + 1 | 9x^3 + 24x^2 + 28x + 7
- (9x^3 + 3x^2)
-------------------
21x^2 + 28x
- (21x^2 + 7x)
----------------
21x + 7
Step 6: Repeat the process of dividing and multiplying until there are no terms left to bring down.
3x^2 + x + 7
_____________________
3x + 1 | 9x^3 + 24x^2 + 28x + 7
- (9x^3 + 3x^2)
-------------------
21x^2 + 28x
- (21x^2 + 7x)
----------------
21x + 7
- (21x + 7)
--------------
0
Step 7: The final result is the quotient: 3x^2 + x + 7.
Therefore, the result of 9x^3 + 24x^2 + 28x + 7 divided by 3x + 1 is 3x^2 + x + 7.