SOLUTION: (x^3-7x^2+13x+3) � (x-2) I'm having difficulty with synthetic division. How do i find the quotient and the remainder in this problem? Can you also be explicit in the steps ple

Question 148168: (x^3-7x^2+13x+3) � (x-2)
I'm having difficulty with synthetic division. How do i find the quotient and the remainder in this problem? Can you also be explicit in the steps please.
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 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	\|	1	-7	13	3
	\|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)

2	\|	1	-7	13	3
	\|
		1

Multiply 2 by 1 and place the product (which is 2) right underneath the second coefficient (which is -7)

2	\|	1	-7	13	3
	\|		2
		1

Add 2 and -7 to get -5. Place the sum right underneath 2.

2	\|	1	-7	13	3
	\|		2
		1	-5

Multiply 2 by -5 and place the product (which is -10) right underneath the third coefficient (which is 13)

2	\|	1	-7	13	3
	\|		2	-10
		1	-5

Add -10 and 13 to get 3. Place the sum right underneath -10.

2	\|	1	-7	13	3
	\|		2	-10
		1	-5	3

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

2	\|	1	-7	13	3
	\|		2	-10	6
		1	-5	3

Add 6 and 3 to get 9. Place the sum right underneath 6.

2	\|	1	-7	13	3
	\|		2	-10	6
		1	-5	3	9

Since the last column adds to 9, we have a remainder of 9. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 3 coefficients (1,-5,3) form the quotient

and the last coefficient 9, is the remainder, which is placed over like this

Putting this altogether, we get:

So

which looks like this in remainder form:
remainder 9

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

RELATED QUESTIONS
Tutor how do I do this problem:* Use synthetic division to find the quotient and the... (answered by ankor@dixie-net.com)

Use synthetic division to find the quotient and the remainder. f(x) = 2x^3 - x^2 +3x - (answered by richwmiller)

Use synthetic division to find the quotient and remainder when dividing p(x)=x^3+x^2-x+2 (answered by Edwin McCravy)

Use either long or synthetic division to divide 4x^3-7x+6 by x+2. Indicate the quotient... (answered by RAY100)

Use synthetic division to find the quotient and the remainder. (x^5+x^3-x^2) divided by... (answered by josgarithmetic,MathTherapy)

use synthetic division to find the quotient and remainder... (answered by stanbon)

Use synthetic division to find the quotient and the remainder of... (answered by cigany29)

Use synthetic division and the Remainder Theorem to evaluate P(c), where... (answered by josgarithmetic)

Find the quotient and remainder using synthetic or long division... (answered by math_helper)