SOLUTION: find the values of A, B and C if (x-1), (x+2), and (x-2) are factors of 2Ax^3-Bx^2-Cx-16

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the values of A, B and C if (x-1), (x+2), and (x-2) are factors of 2Ax^3-Bx^2-Cx-16      Log On


   

Question 1170400: find the values of A, B and C if (x-1), (x+2), and (x-2) are factors of
2Ax^3-Bx^2-Cx-16
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


2Ax%5E3-Bx%5E2-Cx-16+=+k%28x-1%29%28x%2B2%29%28x-2%29+=+k%28x%5E3-x%5E2-4x%2B4%29

The constant term is 4k = -16, so k = -4. Then

2Ax%5E3-Bx%5E2-Cx-16+=+-4x%5E3%2B4x%5E2%2B16x-16

Equating coefficients of each terms gives

2A = -4, so A = -2
-B = 4, so B = -4
-C = 16, so C = -16