Download Aim #44: How do factor out the greatest monomial common factor

Aim #44: How do factor out the greatest monomial common factor?
Homework: Handout
Do Now:
1. Write expressions for the areas of the two rectangles in the figures
given below.
2. Now write an expression for the area of this rectangle:
The total area of this rectangle is represented by 3a
the dimensions of the total rectangle.
2
+ 3a. Find expressions for
When factoring a polynomial, we first look for a monomial that is the greatest
common factor (GCF) of all the terms of the polynomial. Then we reverse the
distribution process by factoring the GCF out of each term and writing it on the
outside of the parentheses.
State the greatest common factor of each of the following.
3
1. 10, 15
5
2
2. 8a , 12a
3 4
4
4. x y, x y
3. 18, 24, 30
3
5. 12x , 6x , 24x
3 2
5
3 2
6. 10a b , 4ab , 8a b c
Factor each by factoring out the Greatest Common Factor.
1. 10ab + 5a
2
2 3
5. 27y + 18y
2 2
8. .75ax + .5bx
2
13. 3x(x + 2) – 4(x + 2)
4
6. 6x y + 9xy + 18y
2
7. 2.1b - 1.5a
2
3. 3g h - 9g h + 12h
2
4. 6y + 18
10. .2x + .4x
3
2. 4x + 12
2
5
3
2 4
9. 2x y - 8xy + 10x y
2
11. 5ab + 6b + 10a b
12. .8abc + .64dbc
14. -2x(x - 5) + 3y(x - 5)
2
15. 2a b + 4ab
2
2
4
16. 4x - 2x
2
17. 16x - 32x
2
18. -32y - 24y
3
2
19. 6x yz + 2xy z - 4xyz
Factor each by factoring out the Greatest Common Factor:
a)
b)
Rewrite the following expressions as the product of 2 binomials by first factoring
out a common binomial factor.
a.
(x - 7)(x - 9) + (x - 7)(4x + 5)
b. (2x - 1)(3x + 5) - (2x - 1) (x + 4)
Let's sum it up!
To factor out a GCF:
1) find the GCF by finding the biggest number that goes into all of the numbers
evenly, and the biggest variable that we can divide out from each term.
2) We write the GCF on the outside of the parentheses, and then divide the
inside terms by the GCF.
3) We can check our work by using distribution.