急!急! F4 Polynomials 2

27) Suppose that the remainder is Ax + B where A and B are constants, then:

f(x) = (x - 5)(x + 2)Q(x) + Ax + B where Q(x) is some poly in x.

f(5) = 9

5A + B = 9 ... (1)

f(-2) = -5

-2A + B = -5 ... (2)

Solving, A = 2 and B = -1

So the remainder is 2x - 1

28a) From the given we have:

f(x) = (x + 1)(x - 3)Q(x) + 2x - 4 where Q(x) is some poly in x.

f(-1) = -2 - 4 = -6

f(3) = 6 - 4 = 2

b) f(-1) = -6

-3 + m + n - 7 = -6

m + n = 4 ... (1)

f(3) = 2

81 + 9m - 3n - 7 = 2

9m - 3n = -72

3m - n = -24 ... (2)

c) Solving equations in (b): m = -5 and n = 9

29a) Sub x = -1 into x2008 + 3, remainder = 4

b) By the result of (a):

Remainder of 62008 + 3 divided by 6 + 1 is 4

So after (62008 + 3) days, it will be Wednesday.