Assignment 21 The Rational Root Theorem (2A.3.4a) Homework: Pg.94 (1-8) Warm Up Solve a. ! − 3 = 28 b. ! + 6 + 32 = 25 Notes ( + 3)( ! + 4 − 1) can be rewritten as ! + 7 ! + 11 − 3 if you multiply the factors out. If you were to factor ! + 2 ! − 5 − 6, which of the following could be possible factors: ( − 3) + 3 ( − 7) ( − 4) ( − 1) ( − 6) + 12 ( − 2) ( − 5) ( + 1) Be able to explain why. Rational Root Theorem If ! ! is a rational root of the polynomial ! ! + ⋯ + ! = 0 with integer coefficients, then p must be a factor of ! and q must be a factor of ! . Finding the roots of higher degree polynomials: 1) Find p (factors of the constant) 2) Find q (factors of the leading coefficient) 3) List all the possible rational roots: ± ! ! 4) Use synthetic division to find the roots (remainder = 0) 5) Factor down to the quadratic, then solve