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Presentation transcript:

Day 1 Lesson Essential Question: How can I use a variety of methods to completely factor expressions and equations?

Warm Up Multiply the following binomials. (x+3)(x-2) (x-5)(x-1) x2+x-6 EQ: How can I use a variety of methods to completely factor expressions and equations?

FOIL First (x –6)(x –3) Outer (x –6)(x –3) Inner Last (x –6)(x –3) EQ: How can I use a variety of methods to completely factor expressions and equations?

FOIL Now YOU try!! First Outer Inner Last (x +2)(x +4) (x +2)(x +4) EQ: How can I use a variety of methods to completely factor expressions and equations?

What do these factors help us find? EQ: How can I use a variety of methods to completely factor expressions and equations?

Graph this on your calculator. When a soccer ball is kicked into the air, how long will the ball take to hit the ground? The height h in feet of the ball after t seconds can be modeled by the quadratic function h(t) = –16t2 + 32t. In this situation, the value of the function represents the height of the soccer ball. When the ball hits the ground, the value of the function is zero. Graph this on your calculator. EQ: How can I use a variety of methods to completely factor expressions and equations?

How would you define the zero of a function? EQ: How can I use a variety of methods to completely factor expressions and equations?

Factoring when a=1 EQ: How can I use a variety of methods to completely factor expressions and equations?

Factoring Find the zeros of f(x) = x2 – 6x + 8 by factoring. EQ: How can I use a variety of methods to completely factor expressions and equations?

Methods of Factoring Worksheet EQ: How can I use a variety of methods to completely factor expressions and equations?

Do #1-3 with a partner on the “Factoring Practice” Worksheet. EQ: How can I use a variety of methods to completely factor expressions and equations?

Check Your Work by Foiling! 1. (x + 9)(x + 2) 2. (y – 7)(y + 5) 3. (g – 6)(g + 2) Check Your Work by Foiling! EQ: How can I use a variety of methods to completely factor expressions and equations?

Difference of Squares When we use it: Usually in the form ax2 – c Both a and c are perfect squares (the square root of each number is a whole number) Difference of Squares EQ: How can I use a variety of methods to completely factor expressions and equations?

Difference of Squares Find the zeros of f(x)=h2-81 by factoring. EQ: How can I use a variety of methods to completely factor expressions and equations?

Difference of Squares Find the zeros of f(x)=49j2-144 by factoring. EQ: How can I use a variety of methods to completely factor expressions and equations?

Methods of Factoring Worksheet EQ: How can I use a variety of methods to completely factor expressions and equations?

Difference of Squares Practice Do #4-10 with a partner on the “Factoring Practice” Worksheet. Difference of Squares Practice EQ: How can I use a variety of methods to completely factor expressions and equations?

Factoring (when a ≠ 1):The Welsh Method Steps: Multiply c and a Rewrite the expression with the new value for c Write (ax + )(ax + ) Finish “factoring” the new expression Reduce each set of parentheses by any common factors Factoring (when a ≠ 1):The Welsh Method EQ: How can I use a variety of methods to completely factor expressions and equations?

Factoring (when a ≠ 1):The Welsh Method Find the zeros of f(x) = 3x2 + 5x - 2 by factoring. Factoring (when a ≠ 1):The Welsh Method EQ: How can I use a variety of methods to completely factor expressions and equations?

Factoring (when a ≠ 1):The Welsh Method Find the zeros of f(x) = 7x2 - 5x - 2 by factoring. Factoring (when a ≠ 1):The Welsh Method EQ: How can I use a variety of methods to completely factor expressions and equations?

Methods of Factoring Worksheet EQ: How can I use a variety of methods to completely factor expressions and equations?

Factoring (when a ≠ 1):The Welsh Method Do #11-16 with a partner on the “Factoring Practice” Worksheet. Factoring (when a ≠ 1):The Welsh Method EQ: How can I use a variety of methods to completely factor expressions and equations?

GCF (Greatest Common Factor) When we use it: all the terms share 1 or more factors Factoring out GCFs save us time!!! 4x2 – 196 = 0 (2x + 14)(2x – 14) = 0 GCF (Greatest Common Factor) EQ: How can I use a variety of methods to completely factor expressions and equations?

GCF (Greatest Common Factor) Steps: Identify any common factor(s) (including the GCF) Factor out the common factor(s) Factor the remaining expression if possible GCF (Greatest Common Factor) EQ: How can I use a variety of methods to completely factor expressions and equations?

GCF (Greatest Common Factor) Find the zeros of f(x) = 4x2 -32x +64 by factoring. GCF (Greatest Common Factor) EQ: How can I use a variety of methods to completely factor expressions and equations?

GCF (Greatest Common Factor) Find the zeros of f(x)= 3x4-24x3+21x2 by factoring. GCF (Greatest Common Factor) EQ: How can I use a variety of methods to completely factor expressions and equations?

Methods of Factoring Worksheet EQ: How can I use a variety of methods to completely factor expressions and equations?

GCF (Greatest Common Factor) Do #17-27 with a partner on the “Factoring Practice” Worksheet. GCF (Greatest Common Factor) EQ: How can I use a variety of methods to completely factor expressions and equations?

GCFs and The Welsh Method EQ: How can I use a variety of methods to completely factor expressions and equations?

Methods of Factoring Worksheet EQ: How can I use a variety of methods to completely factor expressions and equations?

GCFs and The Welsh Method Do #28-33 with a partner on the “Factoring Practice” Worksheet. GCFs and The Welsh Method EQ: How can I use a variety of methods to completely factor expressions and equations?

Picking the Right Method -?!?- 34. x2 + 10x + 16 NOTE: WE HAVE 3 TERMS AND a=1 !! Picking the Right Method -?!?- EQ: How can I use a variety of methods to completely factor expressions and equations?

Picking the Right Method -?!?- 35. 5t2 + 28t + 32 NOTE: WE HAVE 3 TERMS AND a≠1 !! Picking the Right Method -?!?- EQ: How can I use a variety of methods to completely factor expressions and equations?

Picking the Right Method -?!?- NOTE: WE HAVE 2 TERMS WITH A MINUS IN THE MIDDLE AND BOTH TERMS ARE A PERFECT SQUARE !!!!!!! Picking the Right Method -?!?- EQ: How can I use a variety of methods to completely factor expressions and equations?

Picking the Right Method -?!?- Do #36-44 with a partner on the “Factoring Practice” Worksheet. Picking the Right Method -?!?- EQ: How can I use a variety of methods to completely factor expressions and equations?

Exit Ticket Find the zeros. x2-8x-48 4x2-49 2x2+x-3 EQ: How can I use a variety of methods to completely factor expressions and equations?

Warm Up Factor Completely (5 minutes) x2-13x+36 x2-144 (x-4)(x-9) EQ: How can I use a variety of methods to completely factor expressions and equations?