Remark
What value of k will make the entire polynomial = 0 when k is meant to be a factor? In brief, solve the polynomial when f(-3) is substituted into the right hand side.
f(x) = 2x3+x2+kx+18
f(-3) = 2x3+x2+kx+18
f(-3) = 2(-3)^3 + (-3)^2 - 3k + 18 = 0
-54 + 9 - 3k + 18 = 0
-54 + 9 + 18 - 3k = 0
-27 - 3k = 0
- 3k = 27
k = 27/ - 3 = - 9
Answer
k = -9
Check
2x^3 + x^2 - 9x + 18 = 0
2(-3)^3 + (-3^2) - 9(-3) + 18 = 0
-54 + 9 + 27 + 18 = 0 Just as it should be.
