The polynomial f (x) = A(x - 1)? +B(x + 2) is divided by x + 1 and x-2. The remainders are 3 and -15 respectively. Find the values of A and B.

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

answer: r there any options?

step-by-step explanation: