SOLUTION: x^2+3x+1 ________ x-3

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Question 118515: x^2+3x+1
________
x-3
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 x.

so our test zero is 3


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.
3|131
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
3|131
|
1

Multiply 3 by 1 and place the product (which is 3) right underneath the second coefficient (which is 3)
3|131
|3
1

Add 3 and 3 to get 6. Place the sum right underneath 3.
3|131
|3
16

Multiply 3 by 6 and place the product (which is 18) right underneath the third coefficient (which is 1)
3|131
|318
16

Add 18 and 1 to get 19. Place the sum right underneath 18.
3|131
|318
1619

Since the last column adds to 19, we have a remainder of 19. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 2 coefficients (1,6) form the quotient



and the last coefficient 19, is the remainder, which is placed over like this





Putting this altogether, we get:



So

which looks like this in remainder form:
remainder 19


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

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