Question

Can someone thoroughly explain Synthetic Division to me? i mean, -Very- thorough. Polynomial Synthetic division.

Answer 1

its simple enough, the setup is usually whats a bit odd at first

Answer 2

But i dun get it ;_;

Answer 3

provide an example that we can work thru

Answer 4

\[x^2+8x+15 \div x+3\]

Answer 5

a simple one...

Answer 6

good, now synthD is all about format; so use something that suits you the best

Answer 7

first we look at the top part, the numerator, and make sure all the positions are filled in

in this case we start with an x^2; we should have positions for x^1 and x^0, if not use a 0 as a placeholder

Answer 8

this one has all the positions filled in so we are good in that regards

Answer 9

does this make sense?

Answer 10

hmm, yes it does
i suppose, yes

Answer 11

thank you ^W^

Answer 12

fill this in for me then so i can see how well your grasping this first step:

x^4 + x^2 + 2

Answer 13

alright, so the coefficients are...
0 0 2
right?

Answer 14

we would need to fill in two extra zeros, yes; now the format part. I find it easiest to leave in the variables;

Answer 15

x^4 + 0 + x^2 + 0 + 2

Answer 16

i see no sens ein stripping away the variables and making extra work; we dont use them, but they dont get in the way either

Answer 17

it would be something like
l 0 0 0 0 2
---------
i think it was?

Answer 18

something like that. but lets go back to yours

step 2, find what I call a "root"; what makes the denominator a zero?

Answer 19

errr...um, it's opposite value maybe?

Answer 20

like, 1 and -1?

Answer 21

x+3 = 0 when x = ?

Answer 22

well, x would equal -3

Answer 23

then lets make the "root" = -3 forget about trying to remember x+c and negate the c stuff

Answer 24

now for the set up; becuase the rest is just add , multiply, add, multiply etc ...

Answer 25

poly in this row
0 <-----add this row
----------------
r ) <-----multiply this row

Answer 26

i leave the variables in; but we just work the coeffs

x^2 +8x +15
0
-------------
-3 )

Answer 27

if we wanted we could reduce the powers as we go and get the final result; but thats neither here not there

Answer 28

alright then

Answer 29

i think i may have it... maybe

Answer 30

lets work this thru then, and maybe one more example

Answer 31

first we add, what is 1 + 0?

Answer 32

1

Answer 33

x^2 +8x +15
0
-------------
-3 ) 1

what is -3 * 1?

Answer 34

-3

Answer 35

x^2 +8x +15
0 -3
-------------
-3 ) 1

what is 8 - 3?

Answer 36

5

Answer 37

x^2 +8x +15
0 -3
-------------
-3 ) 1 5

what is -3 * 5?

Answer 38

-15

Answer 39

x^2 +8x +15
0 -3 -15
-------------
-3 ) 1 5 0

and 15-15 = 0 and we are done with it

Answer 40

Ohhhhh...Ok, this makes sense now, Thank you so much!

Answer 41

if we had reduced the powers as we went:

x^2 +8x +15
0 -3 -15
-------------
-3 ) 1x +5 R0

x+5 , remainder of zero

Answer 42

dont confuse format for operation; format is what makes things simpler for you to work with. therefore format it to what you are camfortable with :)

Answer 43

lets do another one just to clinch it up

Answer 44

or not, its up to you :)