Question 1187144
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.


<a href = "https://www.purplemath.com/modules/synthdiv.htm" target = "_blank">https://www.purplemath.com/modules/synthdiv.htm</a>


see my synthetic division worksheet below.


<img src = "http://theo.x10hosting.com/2021/110303.jpg" >


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.


<img src = "http://theo.x10hosting.com/2021/110404.jpg" >