SOLUTION: Please help me... Divide 4x^3-3x^2+x+1 / x+2. Thank you

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Question 112188: Please help me... Divide 4x^3-3x^2+x+1 / x+2. Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let's simplify this expression using synthetic division


Start with the given expression %284x%5E3+-+3x%5E2+%2B+x+%2B+1%29%2F%28x%2B2%29

First lets find our test zero:

x%2B2=0 Set the denominator x%2B2 equal to zero

x=-2 Solve for x.

so our test zero is -2


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.
-2|4-311
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 4)
-2|4-311
|
4

Multiply -2 by 4 and place the product (which is -8) right underneath the second coefficient (which is -3)
-2|4-311
|-8
4

Add -8 and -3 to get -11. Place the sum right underneath -8.
-2|4-311
|-8
4-11

Multiply -2 by -11 and place the product (which is 22) right underneath the third coefficient (which is 1)
-2|4-311
|-822
4-11

Add 22 and 1 to get 23. Place the sum right underneath 22.
-2|4-311
|-822
4-1123

Multiply -2 by 23 and place the product (which is -46) right underneath the fourth coefficient (which is 1)
-2|4-311
|-822-46
4-1123

Add -46 and 1 to get -45. Place the sum right underneath -46.
-2|4-311
|-822-46
4-1123-45

Since the last column adds to -45, we have a remainder of -45. This means x%2B2 is not a factor of 4x%5E3+-+3x%5E2+%2B+x+%2B+1
Now lets look at the bottom row of coefficients:

The first 3 coefficients (4,-11,23) form the quotient

4x%5E2+-+11x+%2B+23

and the last coefficient -45, is the remainder, which is placed over x%2B2 like this

-45%2F%28x%2B2%29



Putting this altogether, we get:

4x%5E2+-+11x+%2B+23%2B-45%2F%28x%2B2%29

So %284x%5E3+-+3x%5E2+%2B+x+%2B+1%29%2F%28x%2B2%29=4x%5E2+-+11x+%2B+23%2B-45%2F%28x%2B2%29

which looks like this in remainder form:
%284x%5E3+-+3x%5E2+%2B+x+%2B+1%29%2F%28x%2B2%29=4x%5E2+-+11x+%2B+23 remainder -45


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