Ask Question
22 April, 16:09

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

+3
Answers (1)
  1. 22 April, 16:28
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers