Download 8.5: Factoring using GCF

8.5: Factoring using GCF
Algebra 1: January 22, 2015
Talk between your neighbors and find
the most common piece between the
following
1.) 3,9,54
2.) 4x,12 x 2 ,16 x 4
3.) 6 w2 , 24 w4 ,30w5
What do we call the “common piece”?
Factoring!
• Possible the most important math concept you
will see in high school (other than solving)
• We will learn multiple ways to factor
• Factor means to “un-multiply”
• GCF – Greatest common factor: ALWAYS FIRST
and we will take out everything we can
• We will learn the rest throughout the rest of our
chapter
• GCF will be like “un-distribute”
What a problem looks like…
Suggestions: Break it down – numbers first then variables
4 x  12 x  8 x
4
3
2
1.) All terms are divisible by 4 – part of our GCF is 4
4 x  12 x  8 x  4  x  3 x  2 x
4
3
2
4
3
2

2.) All terms have x’s – take our the “most” (the smallest exponent)
4 x  12 x  8 x  4  x  3x  2 x   4 x  x  3x  2 
4
3
2
4
3
2
2
2
A few together!
6
5
1) 8𝑥 + 4𝑥 + 12𝑥
2
3
2
2) 5𝑐 − 25𝑐 + 10𝑐
Your Turn!
1.) 𝑦 3 – 28𝑦 2 + y
3.) 4𝑎2 b + 28a𝑏 2 + 7ab
2.) 4x + 12𝑥 2 + 16𝑥 3
Factoring to solve
• So many ideas in math are to solve – and
many of those are when your function = 0
• When a function is factored – set all parts = to
0
• 𝑥 2𝑥 − 3 𝑥 + 1 = 0 gives us 3 solutions
• 𝑥 = 0, 2𝑥 − 3 = 0 𝑎𝑛𝑑 𝑥 + 1 = 0 (solve each)
See a few in action
1.) 4b(b + 4) = 0
2). (y – 3)(y + 2) = 0
3.) (a + 6)(3a – 7) = 0