Divide by factoring numerators and then dividing out common factors.
(7y^3-51y^2-2y+72)/(7y-9)
Start with this:
----------------------
7y - 9)7y³ - 51y² - 2y + 72
Divide 7y into 7y³ and get y². Put that above -51y²
y²
----------------------
7y - 9)7y³ - 51y² - 2y + 72
Multiply y² by (7y - 9), getting 7y³ - 9y² and put that under the
first two terms, and draw a line underneath:
y²
----------------------
7y - 9)7y³ - 51y² - 2y + 72
7y³ - 9y²
----------
Subtract and bring down the next term:
y²
----------------------
7y - 9)7y³ - 51y² - 2y + 72
7y³ - 9y²
----------
-42y² - 2y
Divide 7y into -42y² and get -6y². Put that above -2y
y² - 6y
----------------------
7y - 9)7y³ - 51y² - 2y + 72
7y³ - 9y²
----------
-42y² - 2y
Multiply -6y by (7y - 9), getting -42y² + 54y and put that under the
first two terms, and draw a line underneath:
y² - 6y - 8
----------------------
7y - 9)7y³ - 51y² - 2y + 72
7y³ - 9y²
----------
-42y² - 2y
-42y² + 54y
-----------
Subtract and bring down the next term:
y² - 6y
----------------------
7y - 9)7y³ - 51y² - 2y + 72
7y³ - 9y²
----------
-42y² - 2y
-42y² + 54y
-----------
-56y + 72
Divide 7y into -56y and get -8. Put that above +72
y² - 6y - 8
----------------------
7y - 9)7y³ - 51y² - 2y + 72
7y³ - 9y²
----------
-42y² - 2y
-42y² + 54y
-----------
-56y + 72
Multiply -8 by (7y - 9), getting -56y + 72 and put that under the
first two terms, and draw a line underneath:
y² - 6y - 8
----------------------
7y - 9)7y³ - 51y² - 2y + 72
7y³ - 9y²
----------
-42y² - 2y
-42y² + 54y
-----------
-56y + 72
-56y + 72
---------
Subtract and get 0:
y² - 6y - 8
----------------------
7y - 9)7y³ - 51y² - 2y + 72
7y³ - 9y²
----------
-42y² - 2y
-42y² + 54y
-----------
-56y + 72
-56y + 72
---------
0
So there is no remainder and the answer is y²-6y-8.
Edwin
