Question

B) The polynomial ax? + bx + c is divided by x - 1, has remainder 2 when divide

Answer 1

Answer:

a = 3, b = -1 and c = -2.

Step-by-step explanation:

By the Remainder Theorem If the remainder is 2 then  f(-1) = 2  ( as its divided by x+1),  and if remainder = 8 then f(2) = 8.

When divide by  x - 1 the remainder = 0 so f(1) = 0.

So we have the system:

a(-1)^2 + b*-1 + c = 2  

a(2)^2 + b * 2 + c = 8

a(1)^2 + b * 1 + c = 0

a - b + c = 2           (A)

4a + 2b + c = 8      (B)

a + b + c = 0           (C)

Adding A and C gives:

2a + 2c = 2    (D)

a + c = 1          (E)

Multiplying A by 2 and adding to B gives:

6a + 3c = 12

2a + c = 4      (F)

Subtract F - E gives:

2a - a = 4 - 1

a = 3

so c = 1 - 3 = -2.

Substituting for a and c in equation C:

3 - b - 2 = 0

b = -1.