If (ax^3+bx^2-5x+2) has (x+2) as a factor and leaves a remainder 12 when divided by (x-2), find the value of A and b respectively...

Question

Was not able to understand the last part where we took both the equations common and solved a and b.

Will be very grateful if you enlighten me on this topic tomorrow I have my annuals... Please hurry

Regards

Answer 1

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