Help:
Divide:
(35b^3+ 25b^2 + 30b +44) divided by (5b + 5)
To divide the polynomial (35b^3 + 25b^2 + 30b + 44) by (5b + 5), you can use the method of long division. Here's how:
Step 1: Arrange the polynomial in descending order of powers of b. If any power of b is missing, write it with a coefficient of zero.
35b^3 + 25b^2 + 30b + 44
Step 2: Divide the first term of the dividend (35b^3) by the first term of the divisor (5b) to get the quotient term. Write this term above the horizontal line.
________
5b + 5 | 35b^3 + 25b^2 + 30b + 44
7b^2
Step 3: Multiply the divisor (5b + 5) by the quotient term (7b^2) and write the result below the dividend.
7b^2
______________
5b + 5 | 35b^3 + 25b^2 + 30b + 44
- 35b^3 - 35b^2
______________
- 10b^2 + 30b
Step 4: Bring down the next term from the dividend, which is 30b.
7b^2 - 2b
______________
5b + 5 | 35b^3 + 25b^2 + 30b + 44
- 35b^3 - 35b^2
______________
- 10b^2 + 30b
- 10b^2 - 10b
______________
40b + 44
Step 5: Divide the new term (-10b^2 + 30b) by the first term of the divisor (5b) to get the next quotient term.
7b^2 - 2b + 8
______________
5b + 5 | 35b^3 + 25b^2 + 30b + 44
- 35b^3 - 35b^2
______________
- 10b^2 + 30b
- 10b^2 - 10b
______________
40b + 44
- 40b - 40
___________
4
Step 6: Since there are no more terms in the dividend, the division is complete. The final quotient is 7b^2 - 2b + 8, and there is a remainder of 4.
Therefore, the result of dividing (35b^3 + 25b^2 + 30b + 44) by (5b + 5) is:
Quotient: 7b^2 - 2b + 8
Remainder: 4