Question

. 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.
ty CAS​

Answer 1

Answer:

a = -1 and b = -12

Step-by-step explanation:

$2x + 3x^2 + ax + b$ . . . . . . . . . . . . . . . . . . . equation (i)

When equation (i) is divided by (x - 2) it leaves remainder 2

Putting x = 2 in equation (i):

2x2 + 3x$2^2$ + 2a + b = 2

=> 2a + b = 2 - 16 = -14 . . . . . . . . . . . . . . . equation (ii)

When equation (i) is divided by (x + 2) it leaves remainder -2

Putting x = -2 in equation (i):

2x(-2) + 3x$(-2)^2$ - 2a + b = -2

=> -2a + b = -2 + 4 - 12 = -10 . . . . . . . . . . . . . . . equation (iii)

Adding equation (ii) and equation (iii)

2b = - 24,  ∴ b = -12

Putting the value of b in equation (ii):

2a - 12 = -14

∴ 2a = -14 + 12 = -2

∴ a = -1