Question

an some one teach me how to find the remainder of a synthetic division
___________
Heres an example 1/ 4 6 -2

Answer 1

@Clarke11 so... what's the divisor and dividend?

Answer 2

or is that the quotient up there? 1/ 4 6 -2

Answer 3

@jdoe0001 its the division problem in synthetic form

Answer 4

hmm? I dunno what the divisor and dividend are..... so... dunno...

Answer 5

what are you looking for again?

Answer 6

@jdoe0001 i'm looking for the remainder I think 1 is the dividend and 4 6 and -2 are the divisors but idk what synthetic form is

Answer 7

hmmm well..... you're looking for the remainder..... in... what though? you see I dunno where we get it :).... do you have any values given to get it?

Answer 8

@jdoe0001 well its multiple choice the possible answers are 9,8,6 and 7

Answer 9

that... doesn't tell us anything though
a synthetic division means there are two polynomials... and I don't see them

Answer 10

@jdoe0001 i dont understand im really confused

Answer 11

well.. how about a quick screenshot of the material?

Answer 12

@jdoe0001 here ya go

Answer 13

I see ... one sec

Answer 14

notice that in a synthetic division
you "drop down" the 1st term of the dividend, 4 in this case
then multiply the divisor 1 times that, 1 * 4
and the product goes on to add "under" the next term
and so on
\(\large \begin{array}{lllllll}
1&|&4&6&-2\\
&|&&4&10\\
\hline\\
&&4&10&{\color{blue}{ 8}}
\end{array}\qquad {\color{blue}{ remainder}}\)

Answer 15

@jdoe0001 wow thats really simple, I understand how to do it but i still dont know what its used for.

Answer 16

@jdoe0001 aw man theres another question the same but they're are 4 terms instead of three do i just do the same

Answer 17

well.. the synthetic division is used to divide a polynomial by a binomial
for example, your polynomials there could have been say

\(\bf {\color{blue}{ 4}}x^2{\color{blue}{ +6}}x{\color{blue}{ -2}} \div x-1\qquad {\color{brown}{ x-1=0\to x={\color{blue}{ 1}}}}\)

Answer 18

so if the binomial had been x+1 then x+1=0 => x= -1
your divisor would have been -1

Answer 19

but that's what it's used for :)

Answer 20

you'd do the same with whatever amount of terms, yes

Answer 21

This time I have to put the quotient in polynomial form -2/2 2 -2 4

so it would be 2x^2+2x-4 right @jdoe0001

Answer 22

well.... the quotient given, is the coefficients
and the variable's degree, gets dropped by 1 for each term from left to right

Answer 23

so if you divided by \(\bf 2x^2+2x-4\) and the quotient was say 3 4 7

that means \(\bf 3x+4\) + the remainder 7, but the 7 may need to be written in fractional form

what are the actual polynomials you divided?

Answer 24

@jdoe0001 Wait i have it wrong Is it 2x^2-2x+4 instead

Answer 25

well.. is that the dividend? what about the divisor?

Answer 26

@jdoe0001 here have a look

Answer 27

\(\large \begin{array}{rrrrrrrlll}
-2&|&2&2&-2&4\\
&|&&-4&4&-4
\\\hline\\
&&2&-2&2&{\color{blue}{ 0}}

\end{array}\)

Answer 28

@jdoe0001 I understand that, but did i put it in polynomial form correctly 2x^2+2x-4

Answer 29

\(\large \begin{array}{rrrrrrrlll}
-2&|&2&2&-2&4\\
&|&&-4&4&-4
\\\hline\\
&&2&-2&2&{\color{blue}{ 0}}\\
&&\downarrow &\downarrow &\downarrow \\
&&2x^2&-2x&+2

\end{array}\)

Answer 30

@jdoe0001 I understand now thanks alot man.

Answer 31

yw