# What is the quotient and remainder for (24b^3 + 16b^2 + 20b + 36)/(4b + 4)

*print*Print*list*Cite

We have to find the quotient and remainder for (24b^3 + 16b^2 + 20b + 36)/(4b + 4)

(24b^3 + 16b^2 + 20b + 36)/(4b + 4)

=> (6b^3 + 4b^2 + 5b + 9)/(b + 1)

Now use long division:

b + 1 | 6b^3 + 4b^2 + 5b + 9 | 6b^2 - 2b + 7

............6b^3 + 6b^2

----------------------------------------

....................... - 2b^2 + 5b + 9

....................... - 2b^2 - 2b

-----------------------------------------

......................................7b + 9

......................................7b + 7

-----------------------------------------

........................................0 + 2

-----------------------------------------

**This gives the quotient as 6b^2 - 2b + 7 and the remainder is 2.**

First, we'll factorize by 4 the numerator and denominator:

4(6b^3 + 4b^2 + 5b + 9)/4(b+1) = (6b^3 + 4b^2 + 5b + 9)/(b+1)

Using the long division, we'll get:

6b^3 + 4b^2 + 5b + 9 | b+1

-6b^3 - 6b^2 | 6b^2 - 2b + 7 (quotient)

------------------

/ -2b^2 + 5b

+2b^2 + 2b

-----------------

/ +7b + 9

-7b - 7

--------------

/ +2 = reminder

**The quotient is: Q(b) = 6b^2 - 2b + 7 and the reminder is: R(b)=2**.