Given 4x^2 + 5x + 6 = A (x+1)^2 + B(X+1) + C find the values of A, B and C

Question

Given 4x^2 + 5x + 6 = A (x+1)^2 + B(X+1) + C find the values of A, B and C

Answer 1

1. Solve the right side by expanding the equation

A(X^2+2X+1) + BX + B + C = AX^2 + 2AX + A + BX + B + C

 

2. Then place similar terms together

Ax^ 2 = 4x^2 so A = 4

 

3. If A = 4, then we can solve for B

2AX + BX = 5X

2(4)X + BX = 5X

8X + BX = 5X so B = -3

 

4. A + B + C = 6

4 - 3 + C = 6

1 + C = 6 so C = 5