synthetic division?

Question

6n^4-33n^3+16n^2+5n-55/n-5

can any one explain what this means

Answer 1

I love these!

You set it up by putting 5 inside a little box _I and the coefficients of the other polynomial beside it.

5_I 6 -33 16 5 -55

______30__-15__5__50_________

6 -3 1 10 -5

You bring the 6 straight down. Then each bottom number gets mult. by the 5 inside the box, putting the results in the 2nd row. Add straight down to get the bottom row.

Answer has highest power of 3, one less than the polynomial you started with. The answer is

6n^3 -3n^2+1n+10 with remainder of -5. Your book may want you to add the remainder on to the answer as a fraction over n-5.

Edited to add: this didn't really line up very well after I entered it.

Answer 2

Synthetic dividion means you use only the coefficients and not the variables when you are solving. For the n-5 you put the opposite number +5 outside the synthetic division and all the other coefficients straight across like so:


.........6 -33 16 5 -55
5 ......... 30 -15 5 50
____________________
..........6 -3 1 10 -5

The top row is all the coefficents like I wrote before - the 5 out there by itself is the 5 from the n-5. You bring the 6 down - you multiply the 6 by that 5 and put the answer under -33. You add -33 and 30 and get -3. You continue that process ; multiply -3 by 5, get -15 and write it under 16, add and you get 1. Continue multiply add, multiply add. OK - so now the last line is 6, -3, 1 10, -5. These are the coefficients of your answer starting with an exponent one less than your problem. Your problem had an exponent of 4 so the 6 is going to have an exponent of 3; and you write down the answer:6n^3-3n^2+n+10 and the remainder is written as a fraction added on so it is + -5/n-5. This goes at the end of the answer. Some teachers would want you to write the +- as a minus sign infront of that fraction..If you have any questions, write them in details and I'll check later.

Answer 3

it means you are dividing 6n^4-33n^3+16n^2+5n-55 by n-5... they want you to find the remainder and quotient. even if you do long division it should not take a long time. give another shot.

Answer 4

(6n^4 - 33n^3 + 16n^2 + 5n - 55)/(n - 5)

5`|`6`-33```16```5`|`-55
```|````30``-15```5`|``50
-------------------------------
```|`6``-3`````1`10`|```-5

ANS :
6n^3 - 3n^2 + 10n R -5
or
6n^3 - 3n^2 + n + 10 - (5/(n - 5))

Answer 5

u would use synthetic devision with brackets. did u mean (6n^4-33n^3+16n^2+5n-55)/(n-5). if so, then use synthetic

Answer 6

Reduce the Given Equation By (n-5)

+5 i +6 -33 +16 +5 -55 ( by Synthetic Division
i +30
--------------------------------------------------------------

Or by Long division.

Synthetic division is a division done using quotificient in the decending order of powers not leaving any powers in between the largest & the least..

-

Answer 7

Use Horner's algorithm (that's what some of the other answers were talking about, with the little box, etc.).

Answer 8

Just try to follow the steps. It involves only the coefficients of the numerators and the constant term in the denominator:

a)
5 |___6__-33___16___5__-55
________________________
________________________

b)
5 |___6__-33___16___5__-55
________________________
_____6___________________


c)
5 |___6__-33___16___5__-55
________ 30______________
_____6___________________

d)
5 |___6__-33___16___5__-55
________ 30______________
_____6___-3________________

e)
5 |___6__-33___16___5__-55
________ 30__-15___________
_____6___-3________________

f)
5 |___6__-33___16___5__-55
________ 30___-15___________
_____6___-3____1___________

g)
5 |___6__-33___16___5__-55
________ 30___-15__5_________
_____6___-3____1___________

g)
5 |___6__-33___16___5__-55
________ 30___-15__5_________
_____6___-3____1__10_________

h)
5 |___6__-33___16___5__-55
________ 30___-15__5___50____
_____6___-3____1__10_________

i)
5 |___6__-33___16___5__-55
________ 30___-15__5___50____
_____6___-3____1__10___-5____


j)
_____6___-3____1__10___-5 is the answer:

6n^3 - 3n^2 + n + 10 - (5 / (n - 5))

Answer 9

I did that in college and never had to use it since that time, I don't remember.