Question

Use Synthetic Division. Show work on how you got your answer.

36.(2b^3 + b^2 - 2b + 3) / (b+1)^-1

Answer 1

@ArkGoLucky Are you thinking???

Answer 2

oh sorry I was doing something else

Answer 3

this doesn't make sense
\[\frac{1}{(b+1)^{-1}}=b+1\]

Answer 4

Do you know how to do synthetic division??? @satellite73

Answer 5

just multiply the big polynomial with b+1

Answer 6

yes, but i cannot write it here
i have tried, but it doesn't work
it is just a technique, take a look at this and it explains well with an example
http://www.purplemath.com/modules/synthdiv.htm

Answer 7

@satellite73 Giving me a website won't help me

Answer 8

(b+1)^-1 =1/(b+1)
polynomial/(1/(b+1) = polynomial * (b+1)

Answer 9

so it's 1/b+1

Answer 10

@ArkGoLucky What goes in the box???

Answer 11

that's not a division, the way it's written.

Answer 12

I know that

Answer 13

\[\frac{ 1 }{ (b+1)^{-1}} = b+1\]

Answer 14

okay so do I right -1 in the box

Answer 15

write

Answer 16

what's 2/(2^-1) ?

Answer 17

what are you doing

Answer 18

2*2

Answer 19

where did you get the 2

Answer 20

1/(2^-1) = 2

Answer 21

I mean it just doesn't look like you're helping me though, @Algebraic!

Answer 22

this is not a division problem as written
\[\frac{2b^3 + b^2 - 2b + 3}{(b+1)^{-1}}=(2b^3 + b^2 - 2b + 3) (b+1)\]

is what @Algebraic! was telling you

Answer 23

do you know what synthetic division is

Answer 24

yes, but this is not a division problem, it is a multiplication problem

Answer 25

exactly it's just called that

Answer 26

so can you help me??? @satellite73 It's stumped me

Answer 27

is the problem
\[\frac{2b^3 + b^2 - 2b + 3}{b+1}
\]??

Answer 28

yea (2b^3 + b^2 - 2b + 3) / (b+1)^-1

Answer 29

list the coefficients of the numerator, put a \(-1\) on the side
2 1 -2 3
-1
_________________

Answer 30

bring down the first 2
2 1 -2 3
-1
_________________
2

Answer 31

then \(2\times -1=-2\) put it here
2 1 -2 3
-1 -2
_________________
2

Answer 32

then \(1-2=-1\) it goes below
2 1 -2 3
-1 -2
_________________
2 -1

Answer 33

then \(-1\times -1=1\)
2 1 -2 3
-1 -2 1
_________________
2 -1

Answer 34

\(-2+1=-1\)

2 1 -2 3
-1 -2 1
_________________
2 -1 -1

Answer 35

\(-1\times -1=1\)
2 1 -2 3
-1 -2 1 1
_________________
2 -1 -1

Answer 36

\(3+1=4\)

2 1 -2 3
-1 -2 1 1
_________________
2 -1 -1 4

you are done

Answer 37

not quite 2b^2 - b - 1 + 4/b+1

Answer 38

polynomial if degree 3 divided by a polynomial of degree 1 is a polynomial of degree 2
your answer is
\[2d^2-d-1+\frac{4}{d+1}\]

Answer 39

it's b lol

Answer 40

but at the risk of repeating what everyone is saying, as you wrote the problem it is NOT A DIVISION because the \((b+1)^{-1}\) in the denominator brings it up in to the numerator

Answer 41

in other words

\[\frac{2b^3 + b^2 - 2b + 3}{(b+1)^{-1}}=(2b^3 + b^2 - 2b + 3) (b+1)\]

Answer 42

no division is indicated, it is a multiplication

Answer 43

You know what the answer is for the long division is the same answer for this problem (synthetic division). Whatever you have leftover is put over the answer; for example: b +1, x-2, etc, so the answer is 4/b+1

Answer 44

i guess there is no point in my repeating what i wrote above, so i will keep quiet

Answer 45

so do you understand the answer is: 2b^2 - b - 1 + 4/ b+1

Answer 46

never reciprocal it ----> b+1/4, because that's wrong

Answer 47

You're missing the point @Firejay5 . Yes in the beginning it's division problem but if you simplify the expression, it becomes a multiplication problem.

Answer 48

@ArkGoLucky It's over with and I am right; it's just another way of doing Long Division