SOLUTION: I need some help on this homework question: (y square + 6y + 4)/(y-8) Thank you!

Question 144712: I need some help on this homework question:
(y square + 6y + 4)/(y-8)
Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's simplify this expression using synthetic division

Start with the given expression

First lets find our test zero:

Set the denominator equal to zero

Solve for y.

so our test zero is 8

Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.

8	\|	1	6	4
	\|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)

8	\|	1	6	4
	\|
		1

Multiply 8 by 1 and place the product (which is 8) right underneath the second coefficient (which is 6)

8	\|	1	6	4
	\|		8
		1

Add 8 and 6 to get 14. Place the sum right underneath 8.

8	\|	1	6	4
	\|		8
		1	14

Multiply 8 by 14 and place the product (which is 112) right underneath the third coefficient (which is 4)

8	\|	1	6	4
	\|		8	112
		1	14

Add 112 and 4 to get 116. Place the sum right underneath 112.

8	\|	1	6	4
	\|		8	112
		1	14	116

Since the last column adds to 116, we have a remainder of 116. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 2 coefficients (1,14) form the quotient

and the last coefficient 116, is the remainder, which is placed over like this

Putting this altogether, we get:

So

which looks like this in remainder form:
remainder 116

You can use this online polynomial division calculator to check your work

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