Question

How do you use synthetic division to find P(2) and P(-1)? P(x) = x^5 - 4x^3 + 2x

I have this so far, but I can't remember how to find P(-1) 2 | 1 0 -4 0 2 0 ........2 4 0 0 4 _____________ ....1 2 0 0 2 | 4 So, P(2) = 4

Answer 1

list the coefficients and put -2 in the box:

1 0 -4 0 2 0

-2

Answer 2

the remainder will be P(2)

Answer 3

do you know the procedure for synthetic division?

Answer 4

1 0 -4 0 2 0

-2

________________________

Answer 5

oops

Answer 6

1 0 -4 0 2 0


-2
-2 4 0 0 -2
_________________________________
1 -2 0 0 2 -2

Answer 7

last line is a mistake. it should be -2*2=-4 and 0 + (-4) = -4 sorry

Answer 8

so P(2)=-4

Answer 9

Oh wow..thank you so much...i just couldn't figure that out

Answer 10

would you like me to write the next one?

Answer 11

same coefficients but this time you put 1 in the box

Answer 12

Yes please..that would help

Answer 13

I'm actually studying for my final

Answer 14

ok list the coefficients again

1 0 -4 0 2 0

1
___________________________________

Answer 15

bring down the one from the top line
1 0 -4 0 2 0

1
___________________________________
1

Answer 16

1*1=1 goes on the second line

1 0 -4 0 2 0

1 1
___________________________________
1

Answer 17

add 0+1=2

1 0 -4 0 2 0

1 1
___________________________________
1 1

Answer 18

1*=1

1 0 -4 0 2 0

1 1 1
___________________________________
1 1

Answer 19

-4+1=-.3

1 0 -4 0 2 0

1 1 1
___________________________________
1 1 -3

Answer 20

1*-3=-3

1 0 -4 0 2 0

1 1 1 -3
___________________________________
1 1 -3

Answer 21

0+-3=-3

1 0 -4 0 2 0

1 1 1 -3
___________________________________
1 1 -3 -3

Answer 22

1*-3=-3

1 0 -4 0 2 0

1 1 1 -3 -3
___________________________________
1 1 -3 -3

Answer 23

2+-3=-1

1 0 -4 0 2 0

1 1 1 -3 -3
___________________________________
1 1 -3 -3 -1

Answer 24

1*-1=-1

1 0 -4 0 2 0

1 1 1 -3 -3 -1
___________________________________
1 1 -3 -3 -1

Answer 25

0+-1=-1

1 0 -4 0 2 0

1 1 1 -3 -3 -1
___________________________________
1 1 -3 -3 -1 -1

Answer 26

done

Answer 27

on the other hand if i had to evaluate P(-1) i would just plug it in because it is easier:
\[P(-1)=(-1)^5 -4(-1)^3 + 2(-1)=-1+4-2=-1\]

Answer 28

okay, so P(-1) = -1

Answer 29

yes this is correct by either calculation