Question

if k is a constant, what is the value of such that the polynomial 2x3+x2+kx+18 is divisible to x+3. Show your complete work

Answer 1

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.