SOLUTION: Divide using synthetic division: (4x^2-13x+5) divided by (x-3)

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Question 183059This question is from textbook Algebra 2
: Divide using synthetic division: (4x^2-13x+5) divided by (x-3) This question is from textbook Algebra 2

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 | 4 -13 5
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 4)

3 | 4 -13 5
|
4

Multiply 3 by 4 and place the product (which is 12) right underneath the second coefficient (which is -13)

3 | 4 -13 5
| 12
4

Add 12 and -13 to get -1. Place the sum right underneath 12.

3 | 4 -13 5
| 12
4 -1

Multiply 3 by -1 and place the product (which is -3) right underneath the third coefficient (which is 5)

3 | 4 -13 5
| 12 -3
4 -1

Add -3 and 5 to get 2. Place the sum right underneath -3.

3 | 4 -13 5
| 12 -3
4 -1 2

Since the last column adds to 2, we have a remainder of 2. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 2 coefficients (4,-1) form the quotient

and the last coefficient 2, is the remainder, which is placed over like this

Putting this altogether, we get:

So

which looks like this in remainder form:
remainder 2