If (ax³+bx²-5x+2) has (x+2) as a factor and leaves a remainder 12 wh

1.	If (ax³+bx²-5x+2) has (x+2) as a factor and leaves a remainder 12 when divided by (x-2) , find the values of a and b.
Answer» Answer: 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

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

Answer»

Answer:

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