Transcript Lesson 6.1

Bellringer
Multiply
1.
2.
3.
4.
5.
(3x)(4x)
-5x(2x)
-2x(-4x)
4(x + 3)
3x(2𝑥 2 - 4)
1.
2.
3.
4.
5.
12𝑥 2
−10𝑥 2
8𝑥 2
4𝑥 + 12
6𝑥 3 − 12𝑥
6.1 Factoring Polynomials
What is factoring?
• The reverse of multiplying
• Means to write an equivalent expression
that is a product of two or more
expressions
Factoring out a common factor
Multiplying
Factoring
5(x + 3) = 5x+15
3a(b2
+ 2) =
3ab2
5x + 15 = 5(x + 3)
2 + 6a = 3a(b2 + 2)
3ab
+6a
Steps:
1. Find the greatest common factor
(GCF). The GCF of like variables,
is the variable to the lowest power.
2. Divide the polynomial by the GCF.
The quotient is the other factor
(the garbage-what’s left over)
3. Express the polynomial as the product
of the quotient and the GCF.
Factor.
2
3𝑥 + 3
GCF = 3
2
𝑥
3
+ 3(1)
2
3(𝑥 + 1)
Factor.
4
5𝑦
3
20𝑦
−
3
GCF: 5𝑦
3
5𝑦
3
5𝑦 (4)
1𝑦 −
3
5𝑦 (1y − 4)
Factor.
2
2
16𝑎 𝑏
2
20𝑎
+
2
GCF: 4𝑎
2
4𝑎
2
4𝑏
2
4𝑎 (5)
+
2
2
4𝑎 (4𝑏 + 5)
Factor.
5
15𝑥
−
4
12𝑥
3
27𝑥
+
2
GCF: 3𝑥
−
2
3𝑥
3𝑥 2 5𝑥 3 − 3𝑥 2 4𝑥 2 + 3𝑥 2 9𝑥 − 3𝑥 2 (1)
2
3
3𝑥 (5𝑥
−
2
4𝑥
+ 9𝑥 − 1)
Factor.
2
3
4𝑚 𝑛
2
2
2𝑚 𝑛
+
+
2
GCF: 2𝑚 𝑛
2
2𝑚 𝑛
2
2𝑛
2
2𝑚 𝑛
2
6𝑚 𝑛
2
2𝑚 𝑛(3)
+
𝑛 +
2
2
2𝑚 𝑛(2𝑛 + 𝑛 + 3)
Assignment
• Pg. 264 #’s 10 – 38 even