devin's reflection

To solve anything bigger than a quadratic

1. Factor by graphing
-must have even number of terms

2. Quadratic form
-must have only 3 terms
-1st term must=2nd exponent x2 last term must be a #
-1-make g=x^exponent/2 so you get g^2+g+#
-2-do quadratic formula factor complete the square
-3-plug in for g

3. rational root theorem
-1-find all possible roots
-p/q where p is all factors of the constant q is the factors of leading coeff.
-2-check to see which roots work in table
-3-do synthetic division to factor all roots that work
-4-solve the quadratic

Ex. x^3+5x^2-4x-20=0
(x^3+5x^2)-(4x+20)=0
x^2(x+5)-4(x+5)=0
(x^2-4)(x+5)=0
X^2-4=0
x^2=4
x=+-2

x+5=0
x=-5

=(2,0)(-2,0)(-5,0)