Function Exercise

Try to answer the exercise below:
  • The sum result of coeficient x3 with coeficient of x2 from the multiply equation as follows (x - 4)(x + 6)(x + 1) is ...........
          (a) 1    (b) 2    (c) 3    (d) 4

Answer:

 (x - 4)(x + 6)(x + 1) 
  = (x2 - 4x + 6x - 24)(x + 1)
  = (x2 + 2x - 24)(x + 1)
  = x3  + x2 + 2x - 24x - 24
  = x3  + 3x2 - 22x - 24

So coeficient of x3 = 1 and coeficient of x2 = 3, so the sum of coefisient result = 1 + 3 = 4 or same as (d)
  • The result of multiplication of (x 2 - 4)(2x 3 - 3x 2 + 4x - 5) can be expressed as  ax 5 + bx 4 + cx 3 + dx2 + ex + f so the calculation of a + e + f - b - c - d = .....
         (a) 6   (b) 5    (c) 4    (d) 3     (e) 2

Answer:
(x 2 - 4)(2x3 - 3x2 + 4x - 5) =
2x5 - 3x4 + 4x3 - 5x2 - 8x3 + 12x2 - 16x + 20 =
2x5 - 3x4 - 4x3 + 7x2 - 16x + 20 =

so coeficient of a = 2, b = -3, c = -4, d = 7, e = -16, f = 20

so the calculation of a + e + f - b - c - d = 2 - 16 + 20 + 3 + 4 - 7 = 6 so the answer is (a)

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