Answer:
A = - 3 , B = - 3
Step-by-step explanation:
given f(x) divided by (x - h) then the remainder is f(h)
Here f(x) is divided by (x + 1) and (x - 2) , then equate f(- 1) and f(2) to respective remainders and solve for A and B
f(- 1) = A(- 1 - 1) + B(- 1 + 2) = 3 , that is
- 2A + B = 3 → (1)
f(2) = A(2 - 1) + B(2 + 2) = - 15 , that is
A + 4B = - 15 → (2)
Multiplying (2) by 2 and adding to (1) will eliminate A
2A + 8B = - 30 → (3)
Add (1) and (3) term by term to eliminate A
0 + 9B = - 27
9B = - 27 ( divide both sides by 9 )
B = - 3
Substitute B = - 3 into (2) and solve for A
A + 4(- 3) = - 15
A - 12 = - 15 ( add 12 to both sides )
A = - 3
Then A = - 3 , B = - 3
