2. Polynomial Functions
P(x) is an expression containing only positive
whole numerical powers of x
The degree of a polynomial is given by the
highest power of the variable x
Division of polynomials is used to factorise
higher degree polynomials into linear factors
so that the number and values of the x-
intercepts can be determined to assist in
graphing
K McMullen 2011
3. Polynomial Functions
When a polynomial P(x) is divided by a
divisor D(x), the results can be written as:
P(x)D(x)=Qx+R(x)D(x)
Q(x) is the quotient
R(x) is the remainder
K McMullen 2011
4. Polynomial Functions
The remainder theorem:
When P(x) is divided by (x-a), the remainder is
P(a)
When P(x) is divided by (ax+b), the remainder
is P(-b/a)
The factor theorem:
When P(a)=0, then (x-a) is a factor of P(x)
When P(-b/a)=0, then (ax+b) is a factor of P(x)
Once a linear factor has been found using the
factor theorem, other factors may be found
using long division
K McMullen 2011
