Question

Find a and b if x4+3x3−2x2+ax+b is divisible by (x2–3x+2)

Answer 1

First factor x² - 3x + 2 → (x - 1) (x - 2) Set each factor equal to zero and solve: x = 1 and x = 2Plug each value into the dividend, This will create two linear equations you can solve using elimination.x = 1 → (1)^4 + 3(1)³- 2(1)² + a(1) + b = 0 → 2 + a + b = 0 → a + b = -2x = 2 → (2)^4 + 3(2)³- 2(2)² + a(2) + b = 0 → 32 + 2a + b = 0 → 2a + b = -32
Subtract the equations: 2a + b = -32- a - b   = -(-2)------------------a = -30  → a + b = -2 → -30 + b = -2 → b = 28Answer: a = -30 and b = 28