Question

Need some help on this equation.
Use synthetic substitution to find
f(3) = 2x^4 - 3x^2 -x +2
When I use synthetic substitution I got 81, which I'm not sure is right. Aren't the synthetic substitution of an equation and direct supposed to be the same?

Answer 1

whats your setup?

Answer 2

the remainder of a synthetic is equal to the direct results ...

Answer 3

remember to zero in the x^3 thats missing
vvv
2x^4 - 3x^2 -x +2




2x^4 + 0x^3 - 3x^2 -x +2
0 6 18 -45 and so on
3 | 2 6 -15 -46

Answer 4

I did f(3) = 2x^4 - 3x^2 - x + 2
2 -3 -1 + 2
3 _____________6_____9___27______________
2 3 8 29 = 87?

Answer 5

is my setup readable? i know it differs from the usual textbook setup ..

Answer 6

I'm a bit confused by it - what did you get for your answer?

Answer 7

i see i got a stray negative ....

Answer 8

2x^4 + 0x^3 - 3x^2 -x +2
0 6 18 45
-------------------------------
3 | 2 6 15 44

the setup should be recognizable, the only thing I have done differently is to retain the variables (they make good reminders), and move the multiplier down to the bottom to relate it to multiplying bottom row values ...

Answer 9

Ah okay, would you continue that set up with multiplying 44 by 3?

Answer 10

yep, and the final would be the +2 tacked onto it :)

Answer 11

So 134 was your answer? That's what I got for my direct substitution so that must be the answer.

Answer 12

Not sure what's going wrong with my synthetic substitution LOL

Answer 13

i see that you forgot to zero out the x^3 term ... synthetic division is very picky about having ALL the coefficients in order.

Answer 14

no room added for
0x^3
f(3) = 2x^4 -3x^2 - x + 2
2 -3 -1 + 2
3 _____________6_____9___27______________
2 3 8 29 = 87?

Answer 15

So where did the 0x^3 come in exactly?
f(3) = 2x^4 - 3x^2 -x +2
Where is it?

Answer 16

do you recall the property, that anything multiplied by 0 is equal to 0? ; and that adding 0 to anything seems rather pointless?

Answer 17

Yes!

Answer 18

a polynomial is defined as:\[P_n(x)=c_ox^n+c_1x^{n-1}+c_2x^{n-2}+...+c_{n-1}~x+c_n\]
ALL of the powers of x have to be present, even if one of the "c" values is 0

Answer 19

\[2x^4 - 3x^2 -x +2 ~~\to~~2x^4\color{red}{+0x^3} - 3x^2 -x +2 \]

Answer 20

now the right side contains all the powers of x from 4 to 0

Answer 21

OH OKAY! For example if I have an equation 7x^3 + 5x ^1 + 2, I have to add in 0x^2 inbetween the 2?

Answer 22

*two

Answer 23

count down from 3 to 0, and compare

3 2 1 0
7x^3 + 5x^1 + 2

since there is not x^2 term, its been zeroed out and simplified; put it back in

3 2 1 0
7x^3 + 0x^2 + 5x^1 + 2

Answer 24

Thank you so much! I understand!

Answer 25

spose we had:

2x^5-3x^2+1 :) we are missing the ^4 and ^3 and ^1 parts, add them back in

Answer 26

good luck

Answer 27

2x^5 +0x^4+0x^3-3x^2 +0x^1 + 1 ? lol thanks