Loading...
The factor theorem Geometric version If f(x) is a polynomial whose graph crosses the x-axis at x=a, then (x
1 Factorise polynomial expressions 2 3 2 Divide a polynomial by a linear or quadratic factor 2 3 3 Apply the remainder theorem 2 3 4 Apply the factor theorem
In this case, The Remainder Theorem tells us the remainder when p(x) is divided by (x - c), namely p(c), is 0, which means (x - c) is a factor of p What we
Corollary (The Factor Theorem) A polynomial f(x) has (x b a) as a factor if and only if f(a) = 0 The Remainder Theorem follows immediately from the definition
Factor Theorem: The value a is a root of the polynomial p(x) if and only if (x?a) is a factor of p(x) Proof: 1 (=?) Assume that a is a root of the
The Factor Theorem Chapter 11 11-4 BIG IDEA If P(x) is a polynomial, then a is a solution to the equation P(x) = 0 if and only if x - a is a factor of
An important consequence of the Factor Theorem is that finding the zeros of a polynomial is really the same thing as factoring it into linear factors
2 Remainder and Factor Theorems Interactive Mathematics Factor theorem state with proof examples and solutions factorise the Polynomials Maths Mutt
4 2 8 - The Factor Theorem 4 2 - Algebra - Solving Equations Leaving Certificate Mathematics Higher Level ONLY 4 2 - Algebra - Solving Equations
remainder and factor theorems to factorise and to solve polynomials that are of degree higher than 2 From the above examples, we saw that a polynomial