Question 360152
This is similar to doing long division with numbers
:
Solve using long division, then CHECK.
(-30+6y^3-28y+y^2) divided by (2y-5)
: 
6y^3 + y^2 - 28y - 30
:
.............___________________
(2y-5)| 6y^3 + y^2 - 28y - 30
:
This is the form you want for long division
Find a value, that when you multiply it 2y, it will = 6y^3, that would be 3y^2
:
..............................3y^2
.............___________________
(2y-5)| 6y^3 + y^2 - 28y - 30
.................6y^3 - 15y^2; 
.................---------------------
................................16y^2 - 28y

We multiplied the divisor by 3y^2 and subtracted, brought down the 28y
:
..............................3y^2 + 8y
.............___________________
(2y-5)| 6y^3 + y^2 - 28y - 30
.................6y^3 - 15y^2; 
.................---------------------
................................16y^2 - 28y
................................16y^2 - 40y
................................-----------------
...............................................+12y - 30
We multiplied the divisor by 8y and subtracted, brought down -30
:
..............................3y^2 + 8y + 6
.............___________________
(2y-5)| 6y^3 + y^2 - 28y - 30
.................6y^3 - 15y^2; 
.................---------------------
................................16y^2 - 28y
................................16y^2 - 40y
................................-----------------
...............................................+12y - 30
...............................................+12y - 30
.....................................................-----------
We multiplied the divisor by 6 and subtracted, no remainder
:
:
The quotient: 3y^2 + 8y + 6
:
Check this, multiply this by the divisor (2y-5) and see what get
:
:
Do you think you can do this now??