How do you find the value of k such that x − 3 is a factor of #x^3 − kx^2 + 2kx − 15#?
1 Answer
Mar 1, 2016
Explanation:
We should attempt synthetic division to find when
The synthetic substitution would be set up as:
#{:(ul3|,1,-k,2k,-15),(ul" ",ul" ",ul" ",ul" ",ul" "),(" "," "," "," ","|"0):}#
Treating the synthetic division like any other synthetic division problem, we see that
#{:(ul3|,1," "-k," "2k," "" "color(red)(-15)),(ul" ",ul" ",ul(" "3" "" "),ul(-3k+9),ul(color(red)(-3k+27))),(" ",1,-k+3,-k+9,"|"0):}#
If the remainder equals
#-3k+27+(-15)=0#
Solve this to see that
Thus,