Algebra 1
Factoring
Solving by Factoring
Warm Up
Factor the following appropriately.
a. x2 – 16
b.
Name__________________
Date___________________
x2 – 3x – 4
Today, we’re going to combine our factoring techniques with the solving techniques we learned yesterday and
perform a process called “Solve by Factoring”
Solving by Factoring
1.
Make sure you set the polynomial __________________________________________
2.
Always look for the ___________ and take that out first
3.
Count the number of terms in the leftovers
If there are ______, use the _________________________________________________ pattern
If there are _______ or _______, factor using the ______________ Method
4.
If any of your parentheses have two terms in them, make sure there’s no special pattern left
5.
Set ____________ factor equal to ___________ and solve separately!
EXAMPLE 1 – Simple Solve by Factoring
Solve the following polynomials by factoring
a.
x2 – 16 = 0
b.
x2 – 5x – 6 = 0
c.
x2 + 2x + 1 = 0
d.
4x2 – 25 = 0
e.
9x2 – 100 = 0
f.
4x2 – 17x + 4 = 0
EXAMPLE 2 – Solve by Factoring
Solve the following polynomials by factoring
a.
x2 + 5x = - 6
b.
x2 + 12 = 7x
c.
x2 – 14x = - 45
d.
4x2 = 9
e.
x2 + 80 = 18x
f.
x2 + 99 = -20x
e.
2x2 + 3x = 9
f.
5x2 + 19x = -12
g.
2x2 + 2 = -5x
h.
–x + x2 = 56
i.
2x2 + 10x – 28 = 0
j.
3x2 – 27x = -42