Can You Help With Alegbra?

Question

Here's the problem:

when x^3+k is divided by x+2, the remainder is known to be -15. Find the numerical value of k.

Thanks for helping and please show your work (so I can actually understand the problem)

:)

Ugg. This is no fun. I have multiple choice answers and here they are:

-7

4

5

8

23

So which is it? -7 or 23

Answer 1

Hi,

If you want to divide x^3 + k by x + 2, you would put -2 out front and coefficients inside. (Remember for missing terms like x^2 and x, you must put a 0x^2 and 0x in their spots to start the problem.)


......____________
.-2.| 1....0....0.....k
.......__________ Copy the 1 below the line.

......____________
.-2.| 1....0....0.....k
.......__________ Multiply the number at the bottom times the
........1........................ out front. Write answer above the line in
................................. next column.


......____________
.-2.| 1....0....0.....k
.......__-2_______ Add this column.
........1.-2

......____________
.-2.| 1....0....0.....k
.......__-2_______
........1.-2
.....................Multiply the number at the bottom times
. ................the -2 out front. Write answer above the line in
.....................the next column.


......____________
.-2.| 1....0....0.....k
.......__-2__4____
........1.-2 Add this column.


......____________
.-2.| 1....0....0.....k
.......__-2__4____
........1.-2 4 Multiply. the number at the bottom times
.................................-2 out front. Write answer above the
.................................line in the next column.

......____________
.-2.| 1....0....0.....k
.......__-2__4__-8__
........1.-2.....4...-15

You were told the remainder had to be negative 15, so
k + -8 = -15 and that solves to k = -7 That's your answer!!

I hope this helps!! :-)

Answer 2

x^3 + k is divided by x +2 remainder is -15
x+2 =o
x = -2
x^3 + k = -15 put x = -2
(-2)^3 +k = -15
-8 +k = -15
k = -15 + 8
k = -7

Answer 3

The answer is -7. The ones who got 23 were using a remainder of positive 15, not negative 15. Their methods were fine, but they read the question too quickly.

Answer 4

Just adding to what others said: the answer is -7. Anyone who got 23 must have missed the minus sign before the 15 in your question.

Answer 5

let's assume: x^3 + k = (ax^2 + bx + x)(x+2) + 15
then: x^3 +k = ax^3 + (b+2a)x^2 + (c+2b)x + 2c + 15

so:
a=1
b+2a = 0
c+2b = 0
k = 2c+15

so b = -2, c = 4, k = 2*4 + 15 = 23

therefore: k = 23

Answer 6

use a calculator sorry i am no help! l0l doing home work and no one u no knows the answer and u need to show ur work good idea i might try that some time l0l!

Answer 7

Try synthetic division
.....1...0...0...k
-2......-2...4..-8
......1...-2..4...k - 8

k - 8 = 15

k = 23

Answer 8

2^3 = 8
k - 8 = -15
k = 7
. . . . x^2 - 2x + 4
x + 2)x^3 . . . . . . . . . . + k
. . . . x^3 + 2x^2
. . . . . . . . - 2x^2
. . . . . . . . - 2x^2 - 4x
. . . . . . . . . . . . . . . 4x
. . . . . . . . . . . . . . . 4x + 8
. . . . . . . . . . . . . . . . . . . k - 8

Answer 9

no