Question

Please help.

Answer 1

Use synthetic division to find P(-3) for P(x) = x^4 - 2x3 - 4x + 4.

Answer 2

what process have you tried?

Answer 3

I don't know which process to try.

Answer 4

synthetic is all about a organizing the data ... its a setup

Answer 5

for starters we want to make sure we have all the exponent parts in order for the process to work

Answer 6

do we have all of them?

Answer 7

I'm pretty sure, yes

Answer 8

lets see if we can verify it

x^4 - 2x^3 - 4x + 4
^^^
there is no x^2 spot

Answer 9

all we do is fill in a placeholder with a 0 coefficient

x^4 -2x^3 +0x^2 -4x + 4

Answer 10

now we can run the setup

Answer 11

start with a 0 in the second row, and add down; 0 + 1 = 1

x^4 -2x^3 +0x^2 -4x + 4
0
-----------------------
-3 ) 1


multiply that -3 by the 1 and use it in the second row; -3*1 = -3

x^4 -2x^3 +0x^2 -4x + 4
0 -3
-----------------------
-3 ) 1

add down, multiply across, repeat ...


x^4 -2x^3 +0x^2 -4x + 4
0 -3 15 -45 ......
-------------------------
-3 ) 1 -5 15 -49 R

Answer 12

That makes sense, yes.

Answer 13

textbooks say to strip off the x parts ... i find it useful to keep them in as a reference; they also tend to put the multiplier up next to the top row which i find cumbersome. You multiply it to the bottom row values. Other than that, the process is what matters

Answer 14

I completely understand, thank you! So that was basically all of it or was there more?

Answer 15

i left the final column for you to try out and complete. Show me what you understand from it

Answer 16

I kind of really understand where you came from for the first several columns, I'm a bit confused from the last one..

Answer 17

each column gets filled in by taking that -3 and multiplying it by the last value found

in this case:

x^4 -2x^3 +0x^2 -4x + 4
0 -3 15 -45 ......
-------------------------
-3 ) 1 -5 15 -49 R
^^ ^^^

-3 times -49, equals 151 fill this into the next column over


x^4 -2x^3 +0x^2 -4x + 4
0 -3 15 -45 151 <-- right there
-------------------------
-3 ) 1 -5 15 -49 R
^^
now add down the column to solve for R

Answer 18

I multiplied -3 and 151 and got 453. I don't think that's what i was supposed to multiply though..

Answer 19

-3, times -49 gets us 151

we then add 4 and 151

Answer 20

155.

Answer 21

thats what i get too, but let me rechk and make sure i didnt do a simple math error along the way

Answer 22

x^4 - 2x3+0x^2 - 4x + 4
0 -3 15 -45 147
-3 1 -5 15 -49

i made a simple mistake, -3 times -49 is 147, not 151

Answer 23

Ahhh, I see.

Answer 24

147 + 4 = 151 for a final result .... i was thinking to far ahead :)

Answer 25

We all make mistakes. But thank you SO much. You explained it a lot better than what my teacher did.

Answer 26

youre welcome, and good luck :)

Answer 27

Do you think you can help out with a couple of other questions?

Answer 28

fraid not, my real job wants me to do some paperwork :/

Answer 29

Poop. Thank you so much though!