polynome factorisation

Using Synthetic Division to Factor Polynomials Steps 1 Use the Rational Zeros Theorem to make the list of all possible rational roots 2 estT possible roots using synthetic division Once you nd a root rewrite the original polynomial with the root you just found factored out using the resulting coe cients from the successful synthetic division

FACTORING POLYNOMIALS First determine if a common monomial factor (Greatest Common Factor) exists Factor trees may be used to find the GCF of difficult numbers Be aware of opposites: Ex (a-b) and (b-a) These may become the same by factoring -1 from one of them 3 12 3 4 3 3 6 6

Factoring is the process of writing a polynomial as the product of two or more polynomials We will do factoring with integer coefficients Polynomials that cannot be factored using integer coefficients are called irreducible over the integers or prime Methods of Factoring A Factoring out the Greatest Common Factor Problem #1 Factor a) 25 x

Factoring Polynomials Any natural number that is greater than 1 can be factored into a product of prime numbers For example 20 = (2)(2)(5) and 30 = (2)(3)(5) In this chapter we’ll learn an analogous way to factor polynomials Fundamental Theorem of Algebra A monic polynomial is a polynomial whose leading coecient equals 1 So

Practice 7 4 Factor completely by factoring out a GCF then factoring the remaining trinomial 1) x x x 2) x x x 3) x x 4) x x x Factor each sum of cubes 5) x 6) x Factor each difference of cubes 7) x 8) x Factor each completely by grouping