SOLUTION: 2x^4 - 8x^2 + 6 divided by 2x + 2

Question 85751: 2x^4 - 8x^2 + 6 divided by 2x + 2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given polynomial

First lets find our test zero:

Set the denominator equal to zero
Solve for x.

so our test zero is -1

Now set up the synthetic division table by placing the test zero in the upperleft corner and placing the coefficients of the numerator to the right of the test zero.(note: remember if a polynomial goes from to there is a zero coefficient for . This is simply because really looks like

-1	\|	2	0	-8	0	6

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

-1	\|	2	0	-8	0	6

		2

Multiply -1 by 2 and place the product (which is -2) right underneath 0

-1	\|	2	0	-8	0	6
			-2
		2

Add -2 and 0 to get -2. Place the sum right underneath -2.

-1	\|	2	0	-8	0	6
			-2
		2	-2

Multiply -1 by -2 and place the product (which is 2) right underneath -8

-1	\|	2	0	-8	0	6
			-2	2
		2	-2

Add 2 and -8 to get -6. Place the sum right underneath 2.

-1	\|	2	0	-8	0	6
			-2	2
		2	-2	-6

Multiply -1 by -6 and place the product (which is 6) right underneath 0

-1	\|	2	0	-8	0	6
			-2	2	6
		2	-2	-6

Add 6 and 0 to get 6. Place the sum right underneath 6.

-1	\|	2	0	-8	0	6
			-2	2	6
		2	-2	-6	6

Multiply -1 by 6 and place the product (which is -6) right underneath 6

-1	\|	2	0	-8	0	6
			-2	2	6	-6
		2	-2	-6	6

Add -6 and 6 to get 0. Place the sum right underneath -6.

-1	\|	2	0	-8	0	6
			-2	2	6	-6
		2	-2	-6	6	0

Since the last column adds to zero, we have a remainder of zero. This means is a factor of

Now lets look at the bottom row of coefficients:

The first 4 coefficients (2,-2,-6,6) form the quotient

Notice in the denominator , the x term has a coefficient of 2, so we need to divide the quotient by 2 like this:

So

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