Question

9. When a polynomial 2x +3x2 + ax + b is divided by (x - 2) leaves remainder 2, and
(x+2) leaves remainder-2. Find a and b.​

Answer 1

Step-by-step explanation:

P(X) = 2x³ + 3x² + ax + b

P(2) = 0 and p(-2) = 0

if P(2) = (2)³ + 3(2)² + a(2) + b = 0

= 16 + 12 + 2a + b = 0

= 2a + b + 28 = 0

2a + b = -28 -------------(1)

if P(-2) = 0 = 2(-2)³ + 3(-2)² + a(-2) + b = 0

= 2(-8) + 3(4) -2a + b = 0

= -16 + 12 - 2a + b = 0

= -2a + b - 4 = 0

= -2a + b = 4 -----------------(2)

2a + b = -28

- 2a + b = 4

——————————

0 + 2B = -24

——————————

b = -12

therefore 2a + b = -28

2a = -28 - b

2a -12 = -28

2a = -28 + 12

2a = -16

a = -8