SOLUTION: hi, i need some help on this please. use synthetic division to find the remainder when x^2-5x-2 is divided by x+3. thank you!!

Algebra.Com
Question 109454This question is from textbook algebra2 with trigonometry
: hi,
i need some help on this please. use synthetic division to find the remainder when x^2-5x-2 is divided by x+3. thank you!! This question is from textbook algebra2 with trigonometry

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 -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|1-5-2
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
-3|1-5-2
|
1

Multiply -3 by 1 and place the product (which is -3) right underneath the second coefficient (which is -5)
-3|1-5-2
|-3
1

Add -3 and -5 to get -8. Place the sum right underneath -3.
-3|1-5-2
|-3
1-8

Multiply -3 by -8 and place the product (which is 24) right underneath the third coefficient (which is -2)
-3|1-5-2
|-324
1-8

Add 24 and -2 to get 22. Place the sum right underneath 24.
-3|1-5-2
|-324
1-822

Since the last column adds to 22, we have a remainder of 22. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 2 coefficients (1,-8) form the quotient



and the last coefficient 22, is the remainder, which is placed over like this





Putting this altogether, we get:



So

which looks like this in remainder form:
remainder 22


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

RELATED QUESTIONS

This question has two parts, and I'm kind of confused on what is the difference in the... (answered by Edwin McCravy)
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 if the first polynomial is... (answered by lwsshak3)
use synthetic division to determine the quotient and remainder.2x^3-5x^2-4x+6 divided by... (answered by Gogonati)
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 when the first polynomial is... (answered by Edwin McCravy)
I need help with this question Use synthetic division to find the remainder (x3-3x+10 (answered by jim_thompson5910)
Use the Remainder Theorem and Synthetic Division to find the remainders in the following... (answered by solver91311)
Need help with the following: Use synthetic division to find the quotient and... (answered by fractalier)