急!急! F4 Polynomials 1

22(a) f(-1) = -2 - a - b = 0

f(2) = 10 - 4a - b = 0

解之得a = 4,b = -6

(b) f(x) = x^3 - 4x^2 + x + 6 = (x + 1)(x - 2)(x - 3)

7 f(-3) = 2f(2)

-27 + 15 + a = 2(a - 2)

a - 12 = 2a - 4

a = -8

10 The dividend is 2x^3 - 3x^2 + x - 50 since it has the hightest degree

The divisor is then 2x^2 + 5x + 20

Notice that 2x^3 - 3x^2 + x - 50 = (2x^2 + 5x + 20)(x - 4) + (x + 30)

So, the quotient is x - 4 and the remainder is x + 30

14(a) f(2a) = 8a^3 + 8a^3 - 10a^3 - 6a^3 = 0

So, x - 2a is a factor of f(x)

(b) x^3 + 2x^2 - 5x - 6 = (x - 2)(x^2 + 4x + 3) = (x - 2)(x + 1)(x + 3)