Name: ____________________ Math 10F&PC H. Date: _________________

Chapter 3 Factors and Products 3.4 Math Lab: Modelling Trinomials as Binomial Products Focus: Explore trinomials with algebra tiles.

We can use the distributive property and an area model to show the product of two 2-digit numbers.

We can use the same process to show the product of two binomials.

Try This: Use only positive algebra tiles. This rectangle represents the trinomial _________________.

Write each side length on the rectangle. __________________, ____________________

Example 1:

Sketch as many and as you need to complete this rectangle to show the

trinomial x2 + 3x + 2.

Write as a product _____________, _______________

Example 2:

Sketch as many and as you need to complete this rectangle to show the

trinomial x2 + 4x + 4.

Write as a product _____________, _______________

Part B This rectangle represents the trinomial _____________ Write each side length on the rectangle.

Write as a product: ( __________ ).( __________ )

Example 3:

Sketch as many and as you need to complete this rectangle to show the

trinomial 2x2 + 7x + 3

Write as a product: ( __________ ).( __________ )

Example 4:

Sketch as many and as you need to complete this rectangle to show the

trinomial 2x2 + 4x + 2

Write as a product: ( __________ ).( __________ )

Example 5: For each set of algebra tiles below: • Write the trinomial. • Write the trinomial as a product.

a) b) c)

The trinomial is:

a) __________________ b) ___________________ c) _____________________

The Product is:

a) __________________ b) ___________________ c) _____________________

Complete Assess your Understanding #’s 1-4 on Pg. 158

Name: ____________________ Math 10F&PC H. Date: _________________

Chapter 3 Factors and Products

Factoring by Grouping - Assignment #4

Ex.

2

2

3 3

( 3 ) ( 3 )

( 3) ( 3)

( 3)( )

x x xy y

x x xy y

x x y x

x x y

2 2

2 2

2 2

8 16 25

( 8 16) 25

( 4) 25

( 4 5 )( 4 5 )

( 5 4)( 5 4)

a a b

a a b

a b

a b a b

or a b a b

Factor each COMPLETELY by “GROUPING”. [SHOW ALL STEPS & CIRCLE ANSWERS!]

1. 3 2 1x x x 2. 5 10 2am a bm b

3. 25 10 3 6m mn m n 4. 22 6 3 9a ab a b

5. 2 2ax bx axy bxy 6. 2 3 6ax x a

7. 856535 yxxy = 8. bdbcdaca 18304575 22

9. zmnncmcmnnzm 2222 2512020150 10. abaab 7216860140 2

11. 3 2a a b a b 12. xyyxx 123164 32

13. 2 22 1 9y y t 14. 2 24 4 36a ab b

15. 2 2 4 4x y y x 16. 1216 22 aabba

17. 2 21 2n nx x 18. 22 2n c cn n

19. 4 32 2x x x 20. 3 4125 125y y y

21. 2 2 2 24 4 6 9a ab b c cd d 22. 33336 88 yxyxx

Bonus: 7 3 41x x x