Question

Find values of k so that each remainder is 3

Answer 1

\[(x^2+kx-17)\div(x-2)\]
the key is 8

Answer 2

1 k -17

2 2 4+2k
______________
1 2+k 13+2k

Answer 3

k=10

Answer 4

do you know synthetic division because that is what i used. the remainder is 13+2k so set
\[13+2k=3\] and solve for k via
\[13+2k=3\]
\[2k=-10\]
\[k=-5\] but my algebra could be wrong.

Answer 5

yeah it is wrong. remainder should be -13+2k
\[-13+2k=3\]
\[2k=26\]
\[k=13\]

Answer 6

1 k -17

2 2 4+2k
______________
1 2+k 13+2k

how u get 4+2k

Answer 7

i multiplied 2 times 2+2k but i think i made a mistake somewhere. in any case the remainder should be -13+2k not 13+2k

Answer 8

let me do it on paper and get it right.

Answer 9

ok now i have it. k = 8

Answer 10

first off is synthetic division clear? i mean do you know what i am doing when i write

1 k -17

2

__________________________

Answer 11

i am dividing using synthetic division. it is pretty easy.


1 k -17

2 2 4+2k

__________________________

1 2+k -13+k

Answer 12

x^2 + kx -17
2 1 1 -17
----------2----4--------
1 2 -13 ?

Answer 13

you forgot that when you get the 2 you have to add 2 + k

Answer 14

you do not know what the "k" is so when you multiply 1 by 2 you get 2, put it in the line under the k and then add to get 2+k
then you multiply 2 + k by 2, get 4+2k and put it under the -17. when you add you get
-13+2k as your remainder

Answer 15

the coefficient of the "x" term is k, not 1

Answer 16

so the set up for the divisions should look like

1 k -17

2

__________________________

Answer 17

1 k -17

2
frist line 1 from what number, k from what number?
I know second line divi by 2

Answer 18

you list the coefficients of
\[x^2+kx-17\] which are
1 k -17

Answer 19

Ok I got it , Thank

Answer 20

ok good. if you don't know synthetic division this would be a pain. so you get a remainder of -13+2k which you set = 3 and solve to get k = 8. that is the correct answer and if you divide
\[\frac{x^2+8x-17}{x-2}\] you will get
\[x+10+\frac{3}{x-2}\] i.e.
\[(x+10)(x-2)+3=x^2+8x-17\]

Answer 21

I kow very well synthetic division ,I just don't understand how divi without don't know k , now I get it , ty