SOLUTION: Solve the problem Find the value of k so that the remainder is -1 when 5x²+kx-25 is divided by x+2.

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Question 1187144: Solve the problem
Find the value of k so that the remainder is -1 when 5x²+kx-25 is divided by x+2.

Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
i get k = -2.

when k = -2, the equation becomes 5x^2 - 2x - 25 divided by x + 2.

i did it by long division, but later discovered i could do it easier by synthetic division.

the reference for synthetic division below explains the procedure.

https://www.purplemath.com/modules/synthdiv.htm

see my synthetic division worksheet below.

first thing i did was bring down the 5.
then -2 * 5 = -10
then k + (-10) = k - 10
then -2 * (k - 10) = -2k + 20
then -25 + (-2k + 20) = -25 - 2k + 20 = -2k - 5
-2k - 5 is the remainder.
set it equal to -1 to get -2k - 5 = -1
add 5 to both sides to get -2k = 4.
divide both sides by -2 to get k = -2.

that's how i got k = -2.

the equation became 5x^2 - 2x - 25 = 0

i used synthetic division to get a remainder of -1 as shown below.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

Solve the problem
Find the value of k so that the remainder is -1 when 5x²+kx-25 is divided by x+2.

Use the REMAINDER THEOREM: .
Since the factor being used is x + 2, it follows that x + 2 = 0____x = - 2.
then becomes:
------ Substituting remainder - 1 for f(- 2)
- 1 = 20 - 2k - 25
- 1 = - 5 - 2k
- 1 + 5 = - 2k
4 = - 2k