Download Intro to Factoring.notebook

Intro to Factoring.notebook
September 21, 2016
Bell Work
Objective
List each form with its notation that a quadratic equation can be written in and explain how that form is helpful.
------------------------Students will learn how factoring can
1.
be used to solve quadratic equations
2.
by practicing at the process of
3.
factoring and examining special
factoring patterns.
Sep 14­8:08 AM
4.3/4.4 Factoring
Sep 12­9:17 AM
9/21
monomial: (one) a number, variable, or a product of a
number & variable
binomial: (two) the sum of two monomials
trinomial: (three) the sum of three monomials
factors: numbers or variables that multiply together
to give you a product
Factoring ax² + bx + c
Step 1­ What makes ax²?
Step 2­ Look at the sign of c…
­ if +, signs are the same
­look at the sign of bx to determine the
sign
­ if –, signs are different
Step 3­ What makes c?
Step 4­ Of those choices, which add to make b?
Ex. 1: 5z2 + 16z + 3
Ex. 2: 3x2 + 5x ­ 12
x² + bx + c = (c + m)(x + n)
= x² + (m + n)x + mn
Aug 10­12:06 PM
Sep 16­8:10 AM
You Practice
You Practice
Factor 2x2 + 5x + 3
Factor, if possible. a. x² – 9x + 20
Sep 14­7:38 AM
b. x² + 3x – 12
Sep 14­7:38 AM
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Intro to Factoring.notebook
Special Factoring Patterns
Difference of Two Squares: a² – b² = (a – b)(a + b)
Perfect Square Trinomial: a² + 2ab + b² = (a + b)²
a² – 2ab + b² = (a – b)²
September 21, 2016
You Practice
Factor p2 ­ 6p + 9
Ex. 3: Factor the expressions.
a. x² – 49 =
b. d² + 12d + 36 =
c. z² – 26z + 169 =
Aug 10­12:15 PM
What do you call a
Sep 14­7:38 AM
A Sandwich!
witch on a beach?
­­Gracie H.
Sep 16­9:16 AM
Sep 16­9:17 AM
roots: the solutions of a quadratic equation
zeros: the values of p and q; what make the equation
equal zero
Zero Product Property
If A and B are expressions and AB = 0,
then A = 0 or B = 0
Ex. 4: Find the zeros of the functions by rewriting the
function in intercept form.
a. y = x² – x – 12
b. y = x² + 12x + 36
Wrap It Up…
1. What is factoring?
2. Are roots and zeros the same thing?
3. What’s another name for a zero?
4. How do you find roots?
Sep 16­8:40 AM
Aug 10­12:16 PM
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Intro to Factoring.notebook
Assignment
P. 256 #15­20 Factor the expression.
15. x2 ­ 36
18. t2 ­ 16t + 64
16. b2 ­ 81
19. x2 + 8x + 16
17. x2 ­ 24x + 144
20. c2 + 28c + 196
September 21, 2016
Homework Help!!
20. c2 + 28c + 196
5. 4u2 + 12u + 5
P. 260 #1­6 Factor the expression. If the expression cannot be factored, say so.
1. 7x2 ­ 20x ­ 3
4. 3x2 + 5x ­ 12
2. 5z2 + 16z + 3
5. 4u2 + 12u + 5
3. 2w2 + w + 3
6. 4x2 ­ 9x + 2
Sep 16­9:06 AM
Sep 21­8:06 AM
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