Factorisation of Polynomials — Chapter Summary

Polynomials are classified by number

Polynomials are classified by number of terms and by degree. A polynomial of one term is called a monomial, of two terms a binomial, and of three term

If f(x) is divided by

If f(x) is divided by a non-zero polynomial g(x), then there exist unique polynomials q(x) and r(x) such that f(x)=g(x)q(x)+r(x), where r(x)=0 or deg

A non

A non-zero polynomial g(x) is a factor of f(x) if and only if there exists a polynomial q(x) such that f(x)=q(x)·g(x). In this case, the remainder is

The value of a polynomial at

The value of a polynomial at x=α is found by substituting α for x throughout the polynomial. For example, for f(x)=x^2+5x+4, the value at x=3 is found

If a polynomial f(x) is divided

If a polynomial f(x) is divided by (x-a), then the remainder is f(a). This is proved using the Division Algorithm by writing f(x)=(x-a)·q(x)+c and the