2.4 factoring polynomials.notebook
September 25, 2013
2.4 Factoring Polynomials
Choose factors of the
constant to substitute
using factor theorem.
Trial and error until you
find the remainder of 0.
ex 1: Factor fully
x3 + 3x 2-13x - 15
ex 2: Factor
x3- 27x + 10
Sep 14­7:42 PM
1
2.4 factoring polynomials.notebook
September 25, 2013
ex 3: factor P(x)=12x 3+28x2-7x-5
Sometimes it's difficult to find a root
Rational Zero Test
all rational zeros are in the form
factors of the constant
factors of the leading coefficient
Sep 14­7:59 PM
2
2.4 factoring polynomials.notebook
ex: 4 Factor
a) 25x2-4
September 25, 2013
Rule for Difference of Squares
A2 - B2 = (A-B) (A+B)
square root of 1st and last term
b) 49m2+100
c) x3-125
Rule for Difference of Cubes
A3 - B3 = (A-B) (A 2+AB+B2)
cube root
square of cube
roots
negative
product
of cube
roots
Sep 26­3:28 PM
3
2.4 factoring polynomials.notebook
d) 8x3+27
September 25, 2013
Rule for Sum of Cubes
A3+B3 = (A+B) (A 2-AB+B2)
e) x3-1
f) 64 + 125x3
factor out common factor
g) 16x3 + 432y3
h) i) (x-y)3 - (x+y)3
Sep 26­3:31 PM
4
2.4 factoring polynomials.notebook
September 25, 2013
Homework 2.4:
p. 176 #6, 7, 9->13
p. 182 #2->5, 8
Sep 14­8:12 PM
5