Question

If ax3+bx2−5x+2 has x+2 as a factor and leaves a remainder 12 when divided by x−2 , find the value of a and b.

Answer 1

Answer:

a=2

Step-by-step explanation:

Let f(x) = ax3 + bx2 - 5x + 2  

Since x+2 is a factor of f(x), f(-2) = 0

   So, -8a + 4b + 12 = 0

Since the remainder is 12 when f(x) is divided by x-2, f(2) = 12  

  So, 8a + 4b - 8 = 12  

We have the system of equations:  -8a + 4b = -12

                                                   8a + 4b = 20  

Add the equations to obtain 8b = 8  

                                         b = 1  

Since b = 1 and 8a + 4b = 20, 8a + 4 = 20  

                                                  8a = 16  

                                                    a = 2

Answer 2

Answer:

Step-by-step explanation:Can’t understand