SOLUTION: If (x-2) is a factor of f(x) = 4x³-19x²+ax-14, find the value of the constant a factorise and solve the polynomial.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If (x-2) is a factor of f(x) = 4x³-19x²+ax-14, find the value of the constant a factorise and solve the polynomial.       Log On


   

Question 1147344: If (x-2) is a factor of f(x) = 4x³-19x²+ax-14, find
the value of the constant a
factorise and solve the polynomial.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Use synthetic division to divide by x - 2

2 | 4   -19     a    -14
  |       8   -22  2a-44 
    4   -11  a-22  2a-58

       Remainder = 2a-58 = 0
                      2a = 58
                       a = 29

        Quotient = 4x²-11x+(a-22)
                 = 4x²-11x+(29-22)
                 = 4x²-11x+7
                 = (4x-7)(x-1)

            f(x) = (x-2)(4x-7)(x-1)

            x-2 = 0;  4x-7 = 0;   x-1 = 0
              x = 2;     x = 7/4;   x = 1

Edwin