SOLUTION: Divide. Use synthetic division if possible (8x^4+5x^3+4x^2-x+7)/(x+1) (12x^3+31x^2-17x-6)/(x+3) i need some major help with these 2 questions. i was given 110 questions, i nee

Question 133344: Divide. Use synthetic division if possible
(8x^4+5x^3+4x^2-x+7)/(x+1)
(12x^3+31x^2-17x-6)/(x+3)
i need some major help with these 2 questions. i was given 110 questions, i need some help with these 2=/
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

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 -1

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.

-1	\|	8	5	4	-1	7
	\|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 8)

-1	\|	8	5	4	-1	7
	\|
		8

Multiply -1 by 8 and place the product (which is -8) right underneath the second coefficient (which is 5)

-1	\|	8	5	4	-1	7
	\|		-8
		8

Add -8 and 5 to get -3. Place the sum right underneath -8.

-1	\|	8	5	4	-1	7
	\|		-8
		8	-3

Multiply -1 by -3 and place the product (which is 3) right underneath the third coefficient (which is 4)

-1	\|	8	5	4	-1	7
	\|		-8	3
		8	-3

Add 3 and 4 to get 7. Place the sum right underneath 3.

-1	\|	8	5	4	-1	7
	\|		-8	3
		8	-3	7

Multiply -1 by 7 and place the product (which is -7) right underneath the fourth coefficient (which is -1)

-1	\|	8	5	4	-1	7
	\|		-8	3	-7
		8	-3	7

Add -7 and -1 to get -8. Place the sum right underneath -7.

-1	\|	8	5	4	-1	7
	\|		-8	3	-7
		8	-3	7	-8

Multiply -1 by -8 and place the product (which is 8) right underneath the fifth coefficient (which is 7)

-1	\|	8	5	4	-1	7
	\|		-8	3	-7	8
		8	-3	7	-8

Add 8 and 7 to get 15. Place the sum right underneath 8.

-1	\|	8	5	4	-1	7
	\|		-8	3	-7	8
		8	-3	7	-8	15

Since the last column adds to 15, we have a remainder of 15. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 4 coefficients (8,-3,7,-8) form the quotient

and the last coefficient 15, is the remainder, which is placed over like this

Putting this altogether, we get:

So

which looks like this in remainder form:
remainder 15

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

# 2

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	\|	12	31	-17	-6
	\|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 12)

-3	\|	12	31	-17	-6
	\|
		12

Multiply -3 by 12 and place the product (which is -36) right underneath the second coefficient (which is 31)

-3	\|	12	31	-17	-6
	\|		-36
		12

Add -36 and 31 to get -5. Place the sum right underneath -36.

-3	\|	12	31	-17	-6
	\|		-36
		12	-5

Multiply -3 by -5 and place the product (which is 15) right underneath the third coefficient (which is -17)

-3	\|	12	31	-17	-6
	\|		-36	15
		12	-5

Add 15 and -17 to get -2. Place the sum right underneath 15.

-3	\|	12	31	-17	-6
	\|		-36	15
		12	-5	-2

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

-3	\|	12	31	-17	-6
	\|		-36	15	6
		12	-5	-2

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

-3	\|	12	31	-17	-6
	\|		-36	15	6
		12	-5	-2	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 3 coefficients (12,-5,-2) form the quotient

So

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

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