Factoring Review
description
Transcript of Factoring Review
![Page 1: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/1.jpg)
Factoring Review
25 January 2011
![Page 2: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/2.jpg)
Factoring The process of rewriting an
equation or expression as the product of its factors
Example: x2 + 3x + 2 = (x + 2)(x + 1)
Most common form is the quadratic form: ax2 + bx + c, a ≠ 0
![Page 3: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/3.jpg)
Factoring (when a = 1)ax2 + bx + c = (x + ___ ) (x + ___ )
multiply to equal c and add up to equal b
You can always check your answer by FOIL-ing!
![Page 4: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/4.jpg)
Finding Factors of C1. Identify the value of c2. On your calculator, go to the y=
screen3. Type C/X into y14. Go to the table5. Any whole numbers (positive,
non-decimal numbers) in the y1 column are factors of c
![Page 5: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/5.jpg)
Example
![Page 6: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/6.jpg)
Example #1
24x11x2
![Page 7: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/7.jpg)
Example #2
35x2x2
![Page 8: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/8.jpg)
Example #3
12x7x2
![Page 9: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/9.jpg)
Your Turn: Complete problems 1 – 4 on the
“Factoring Practice” handout Check your answer by FOIL-ing!
![Page 10: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/10.jpg)
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)
)cxa)(cxa(
cax2
![Page 11: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/11.jpg)
Example #1
81h2
![Page 12: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/12.jpg)
Example #2
144j49 2
![Page 13: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/13.jpg)
Your Turn: Complete problems 5 – 10 on the
“Factoring Practice” handout Remember to check your answer
by FOIL-ing!
![Page 14: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/14.jpg)
Factoring (when a ≠ 1):The Welsh Method Pt. I
1. Multiply c and a2. Rewrite the expression with the new
value for c3. Write (ax + )(ax + )4. Finish “factoring” the new expression5. Reduce each set of parentheses by
any common factors
![Page 15: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/15.jpg)
Example #14y13y3 2
![Page 16: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/16.jpg)
Example #22x5x3 2
![Page 17: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/17.jpg)
Example #32g5g7 2
![Page 18: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/18.jpg)
Your Turn: Complete problems 11 – 20 on the
“Factoring Practice” handout Don’t forget to check by FOIL-ing!
![Page 19: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/19.jpg)
GCF (Greatest Common Factor) When we use it: when the all the
terms share 1 or more factors Factoring out GCFs save us
time!!!
![Page 20: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/20.jpg)
GCF (Greatest Common Factor) Steps:1. Identify any common factor(s)
(including the GCF)2. Factor out the common factor(s)3. Factor the remaining expression if
possible
![Page 21: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/21.jpg)
Example #1x3x2x 23
![Page 22: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/22.jpg)
Example #264x32x4 2
![Page 23: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/23.jpg)
Example #3234 y21y24y3
![Page 24: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/24.jpg)
Your Turn: Complete problems 1 – 10 on
“Functions Practice Pt. II” handout
![Page 25: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/25.jpg)
GCFs and The Welsh Method
20x14x2 2 Make sure you factor out any
GCFs or the Welsh Method
doesn’t work!!!
![Page 26: Factoring Review](https://reader036.fdocuments.us/reader036/viewer/2022070423/568167b9550346895ddd084a/html5/thumbnails/26.jpg)
Your Turn: Complete problems 11 – 22 on the
“Factoring Practice Part II” handout