FACTORING When a Is Not 1
Algebra II Name______
Hr_____
FACTORING EXIT TICKET
Factor. Show all of your work!
1. 2. 3.
Algebra II Name______
Hr_____
FACTORING EXIT TICKET
Factor. Show all of your work!
1. 2. 3.
Algebra II Name______
Factoring Station #1 Hr_____
You are stuck! What do you do? You are not sure how to begin factoring a trinomial that has a coefficient other than 1. The following will get you started.
If the template for a quadratic expression is , then in the polynomial
, a = 2 b = 5 c = -12.
SO a • c or a times c = -24
1. What is a • c in ______
2. What is a • c in ______
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Now that you can find a•c, find the factors of a•c. In the example above, the factors of -24 are
= -24
3. List the factors of ac from #1 4. List the factors of ac from #2
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Now that you have the factors of a•c, determine which factors add to the middle term (b). In the example above, the factors of -24 that add to the middle term (b) are
+8 • -3 because b (the middle term) is +5 and +8 + (-3) = +5
5. From # 3, select which factors add to b (the middle term) ______
6. From # 4, select which factors add to b (the middle term) ______
Algebra II Name ______
Factoring Station #2 Hr_____
You are stuck! What do you do? You understand how to create your table of factors, but you don’t understand how to use GROUPING, SPLITTING the middle, and/or the BOX method to factor. The following instructions will help you factor.
VOCABULARY for factoring:
· GROUPING: a technique used to factor 4 term polynomials by using the GCF (greatest common factor).
· SPLITTING the middle: a technique of factoring done by taking a trinomial and creating a 4 term polynomial and then using GROUPING (see below)
· BOX: a technique of factoring using a box as a visual (see the other side)
GROUPING
Factor this polynomial using the SPLITTING the middle and GROUPING technique.
This is the original trinomial that needs to be factored:
(Remember to find the factors of a • c that add to b.)
This is the “SPLIT” trinomial:
To GROUP the 4 term polynomial follow these steps.
1. Place parentheses around the first two and last two terms of the polynomial
2. Factor out the GCF of the first binomial
3. Factor out the GCF of the last two terms
What is the GCF of each binomial?
GCF: GCF: Factor out the GCFs to create a new binomial (below).
2x + 5 Now, find the GCF of the new binomial and factor.
GCF:
Therefore, your answer is
BOX (similar to GROUPING)
Factor this polynomial using the BOX technique.
This is the original trinomial that needs to be factored:
(Remember to find the factors of a • c that add to b.)
This is the “SPLIT” trinomial:
To use the BOX technique with this 4 term polynomial, place each of the 4 terms into the box as instructed below.
1. Place the first (quadratic) term in the upper left box
2. Place the last (constant) term in the lower right box
3. Place the two middle (linear) terms in the remaining boxes in any order
4. Factor the two rows using the GCF.
5. Factor the two columns using the GCF.
Therefore, is a factor and is the other factor.
So, .
Factor by splitting the middle and grouping or by using the box method.
1. 2. 3.
Algebra II Name ______
Factoring Station #3 Hr_____
You are stuck! What do you do? You understand how to create your table of factors, how to use GROUPING, SPLITTING the middle, and/or the BOX method to set how to factor, but you are struggling with how to finish. The following instructions will help you completely factor.
Remember that factoring is how you can undo the distributive property (or FOIL-ing). So, when you are grouping/splitting the middle or using the box method to factor, realize that your 4-term polynomial is what you would have if you were FOILing two binomials. See below for an example.
Simplify. Factor.
Finish factoring each of the following trinomials.
1.
2.
3.
4.
5.
UNIT 6
(Part I)
Know:
· Definitions
o Quadratic Function
o Terminology for Graphing Functions (see pacing guide)
o Standard, Vertex and Intercept Form
o Factoring
o Extracting the Square
Do:
· Graph quadratics in standard, intercept and vertex form.
· Factor quadratics when a = 1 and a1.
· Solve quadratics by factoring.
· Solve quadratics by extracting the square.
Understand:
· The form of a quadratic function helps to determine the best way to graph the function.
· Transformations are universal in graphing whether it is linear, quadratic, etc.
· Factoring is the inverse of multiplying functions.
Learning Progressions
· Graphing Quadratics
o Vertex Form
o Intercept Form
o Standard Form
· Factoring
o a = 1
o a 1
o Trinomials
o LCD
o Special Binomials
· Solving
o By Factoring
o By Extracting the Square
Formative Assessments w/ DI Activities
· Graphing Quadratics
o Formative Assessment: Give EXIT TICKET which includes one problem of each type of graphing problem (vertex, intercept and standard forms)
§ Grade the exit ticket to determine which students need additional instruction over each type of graphing problem(s).
§ Mark the exit ticket with a number 1, 2, or 3 or combination of those depending upon which type of graphing problem(s) the student needs to work on.
§ Some students may not have a number if they have mastered all three types of problems.
o Differentiated Instruction Activity: Have students complete extra practice worksheet(s) covering the type of graphing problem(s) they did not understand from previous day’s exit ticket.
§ Each worksheet will have guided practice example with explanation in order to facilitate scaffolding.
§ Students who mastered the different types of graphing problems on the formative assessment will begin working on the homework assignment for this section with minimal teacher interaction.
§ Students will know which worksheet(s) to pick up based on the number(s) at the top of their exit ticket which will be returned to them at the beginning of the hour.
§ Students continue to work on the worksheet(s) until is complete and the teacher has checked it. They then begin working on the homework assignment for this section.
§ Students may work in groups (according to the number on the worksheet) or individually.
· Solving Quadratics by Factoring
o Formative Assessment: Students will complete an Exit Ticket. The problem(s) the student has incorrect will determine the level of intervention the student needs to be successful.
§ If the student misses #1 – he has no idea how to factor or can’t even get started on the problem
§ If the student misses #2 – he can get the problem started, but can’t group or use the “box method”
§ If the student misses #3 – he can get started; he can use the group or “box” method, but can’t finish the factoring
o Differentiated Instruction Activity: Students will complete a series of worksheets based upon their performance on the formative assessment. These worksheets must be completed in order as they build on each other.
§ Students will be assigned stations with a scaffolded worksheet to complete for each station. The following process will be used for the stations.
· Misses problem #1 on Exit Ticket – completes all 3 worksheets then begins on homework
· Misses problem #2 on Exit Ticket – completes worksheets 2 and 3 then begins on homework
· Misses problem #3 on Exit Ticket – completes worksheet 3 then begins on homework
· Students who get all problems correct on the Exit Ticket – immediately begin working on the homework assignment
§ Students will know which worksheet(s) to pick up based on the number(s) at the top of their exit ticket which will be returned to them at the beginning of the hour.
§ Students continue to work on the worksheet(s) until is complete and the teacher has checked it. They then begin working on the homework assignment for this section.
§ Students may work in groups (according to the number on the worksheet) or individually.
· Solving Quadratic by Extracting the Square
o Formative Assessment: Students will be given an Exit Ticket and based upon their performance they will be assigned a station(s) the next day which will provide them additional practice and instruction.
§ Grade the exit ticket to determine which students need additional instruction over each type of problem(s).
§ Mark the exit ticket with a number 1, 2, 3, or 4 or combination of those depending upon which type of problem(s) the student needs to work on.
§ Some students may not have a number if they have mastered all four types of problems.
o Differentiated Instruction Activity: Have students complete extra practice worksheet(s) covering the type of solving problem(s) they did not understand from previous day’s exit ticket.
§ Each worksheet will have guided practice example with explanation in order to facilitate scaffolding.
§ Students who mastered the different types of solving problems on the formative assessment will begin working on the homework assignment for this section with minimal teacher interaction.
§ Students will know which worksheet(s) to pick up based on the number(s) at the top of their exit ticket which will be returned to them at the beginning of the hour.
§ Students continue to work on the worksheet(s) until is complete and the teacher has checked it. They then begin working on the homework assignment for this section.
§ Students may work in groups (according to the number on the worksheet) or individually.