More about Polynomials(1)

1)

Degree of a polynomial according to a term of it with the highest number of product of unknowns.

For 2a + 6b - 3abc + 2 - 7a² , the term - 3abc is the product of 3 unknowns
a ,b and c.

So degree = 3.


2)

It is because the degree of remainder must be less then the degree of
the divisor.

So when p(x) is divided by(x+2)(x-1), the degree of (x+2)(x-1) is 2 ,
then the degree of the remainder must less then 2 ,
i.e. the degree of the remainder is 1 or 0.

So we let ax + b be the remainder.

for degree = 1 , a ≠ 0

for degree = 0 , a = 0.

2012-02-19 14:45:50 補充：
We let P(x) = (x-1)(x+2) * Q(x) + ax + b ,

because

P(x) = Divisor * Quotient + remainder