Need help from an expert?
The world’s top online tutoring provider trusted by students, parents, and schools globally.
The factor theorem states that if a polynomial f(x) has a factor (x-a), then f(a) = 0.
The factor theorem is a useful tool in algebraic manipulation of polynomials. It allows us to determine whether a given value is a root of a polynomial, and also to factorise polynomials.
To use the factor theorem, we first need to identify a potential factor of the polynomial. For example, if we have the polynomial f(x) = x^3 - 6x^2 + 11x - 6, we might suspect that (x-1) is a factor. To check this, we evaluate f(1) and see if it equals zero:
f(1) = 1^3 - 6(1)^2 + 11(1) - 6 = 0
Since f(1) = 0, we know that (x-1) is a factor of f(x). We can then use polynomial division or synthetic division to find the other factors of f(x). In this case, we get:
f(x) = (x-1)(x^2 - 5x + 6) = (x-1)(x-2)(x-3)
So the roots of f(x) are x=1, x=2, and x=3.
In summary, the factor theorem is a powerful tool for factorising polynomials and finding their roots. By identifying potential factors and evaluating the polynomial at those values, we can quickly determine whether a given value is a root and factorise the polynomial accordingly.
Study and Practice for Free
Trusted by 100,000+ Students Worldwide
Achieve Top Grades in your Exams with our Free Resources.
Practice Questions, Study Notes, and Past Exam Papers for all Subjects!
The world’s top online tutoring provider trusted by students, parents, and schools globally.