how do you solve this problem?
(24b^3+16b^2+24b+39)/(4b+4)
Are you trying to simplify the equation?
Please check to make sure you don't have a typo
If your question had been
(24b^2 + 16v^2 + 24b + 32)/(4b+4)
then the result would be 6b^2 - 2b + 8
To solve this problem, we need to divide the given polynomial expression (24b^3 + 16b^2 + 24b + 39) by the polynomial expression (4b + 4). This can be done using polynomial long division. Here's how you can approach it step by step:
1. Start by observing the terms with the highest powers of b in the dividend (24b^3) and the divisor (4b). Divide 24b^3 by 4b to get 6b^2.
6b^2
_______
4b + 4 | 24b^3 + 16b^2 + 24b + 39
2. Multiply the divisor (4b + 4) by the quotient obtained in step 1 (6b^2). Place the product (24b^2 + 24b) below the corresponding terms in the dividend.
6b^2
_______
4b + 4 | 24b^3 + 16b^2 + 24b + 39
- (24b^2 + 24b)
3. Subtract the newly obtained polynomial (24b^2 + 24b) from the dividend (24b^3 + 16b^2 + 24b + 39) and bring down the next term (39).
6b^2
_______
4b + 4 | 24b^3 + 16b^2 + 24b + 39
- (24b^2 + 24b)
___________
+ 39
4. Now, repeat the process by identifying the term with the highest power of b in the updated dividend (39) and divide it by the first term in the divisor (4b). Dividing 39 by 4b gives you (39/(4b)) = 9.75/b.
6b^2 + 9.75/b
_______
4b + 4 | 24b^3 + 16b^2 + 24b + 39
- (24b^2 + 24b)
___________
+ 39
5. Multiply the divisor (4b + 4) by the quotient (9.75/b) and place the product (39 + 39/b) below the corresponding terms in the dividend.
6b^2 + 9.75/b
___________
4b + 4 | 24b^3 + 16b^2 + 24b + 39
- (24b^2 + 24b)
___________
+ 39 + 39/b
6. Subtract the newly obtained polynomial (39 + 39/b) from the dividend (24b^3 + 16b^2 + 24b + 39) to obtain the remainder.
6b^2 + 9.75/b
___________
4b + 4 | 24b^3 + 16b^2 + 24b + 39
- (24b^2 + 24b)
___________
+ 39 + 39/b
- (39 + 39/b)
_______________
0
7. Since the remainder is 0, we have successfully divided the polynomial expression.
Therefore, the solution to the problem is:
(24b^3 + 16b^2 + 24b + 39)/(4b + 4) = 6b^2 + 9.75/b
Note: In certain cases, the solution may contain fractions or decimals. Make sure to simplify or rationalize the expression if needed.