SOLUTION: Dividing Polynomials: synthetic 2x^4 - 10x^2 + 6x - 8 divided by x + 3 please help me if you can

Question 85753: Dividing Polynomials: synthetic

2x^4 - 10x^2 + 6x - 8 divided by x + 3
please help me if you can
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 -3

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. This is simply because really looks like

-3	\|	2	0	-10	6	-8

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

-3	\|	2	0	-10	6	-8

		2

Multiply -3 by 2 and place the product (which is -6) right underneath 0

-3	\|	2	0	-10	6	-8
			-6
		2

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

-3	\|	2	0	-10	6	-8
			-6
		2	-6

Multiply -3 by -6 and place the product (which is 18) right underneath -10

-3	\|	2	0	-10	6	-8
			-6	18
		2	-6

Add 18 and -10 to get 8. Place the sum right underneath 18.

-3	\|	2	0	-10	6	-8
			-6	18
		2	-6	8

Multiply -3 by 8 and place the product (which is -24) right underneath 6

-3	\|	2	0	-10	6	-8
			-6	18	-24
		2	-6	8

Add -24 and 6 to get -18. Place the sum right underneath -24.

-3	\|	2	0	-10	6	-8
			-6	18	-24
		2	-6	8	-18

Multiply -3 by -18 and place the product (which is 54) right underneath -8

-3	\|	2	0	-10	6	-8
			-6	18	-24	54
		2	-6	8	-18

Add 54 and -8 to get 46. Place the sum right underneath 54.

-3	\|	2	0	-10	6	-8
			-6	18	-24	54
		2	-6	8	-18	46

Since the last column adds to 46, we have a remainder of 46. This means is a not factor of
Now lets look at the bottom row of coefficients:

The first 4 coefficients (2,-6,8,-18) form the quotient

and the last coefficient 46, is the remainder, which is placed over like this

Putting this altogether, we get:

So

which looks like this in remainder form:
remainder 46

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