1. In this lesson, we will factor polynomials and solve problems using polynomials

2. Model the polynomial with algebra tiles

3. Arrange the model into a rectangle
Add x’s to fill in the rectangle. How do we know they must have opposite signs?

4. Factor the polynomial

5. What two factors could be multiplied to get a product of 3x2 + x – 2 ?
If the area of Janet’s rectangular bedroom is 3x2 + x – 2 , what are the dimensions?
What two factors could be multiplied to get a product of 3x2 + x – 2 ?

6. Factor the polynomial 3x2 + x – 2+1
3x2
-2x
The dimensions of Janet’s bedroom are (3x – 2) by (x + 1) 3x -2

7. If the length of a poster is one inch more than twice the width
If the length of a poster is one inch more than twice the width. Write an expression for the perimeter of the poster in terms of the width, w.

8. First, we will draw a rectangle to represent the poster
Now label the sides. The length is 1 inch more than twice the width
2w+1
2w+1 w

9. To find the perimeter, add the sidesw
The perimeter of the poster in terms of the width is w + 2 inches
2w+1
2w+1 w

10. Factor: 4x2 – 1 Model the polynomial with tiles (2x + 1)(2x – 1)
Can you see a shortcut for factoring this polynomial?

11. 4x2 – 1 is call ‘difference of squares’
(2x + 1)(2x – 1)
If two ‘squares’ are subtracted, the factored form always follows the same pattern
Try another one…
Factor: 9x2 – 4

12. What happens to the middle term when you multiply the two binomials?
9x2 – 4
(3x + 2)(3x – 2)
What happens to the middle term when you multiply the two binomials?

13. Complete Activity 9e
Factor polynomials
Simplify polynomial expressions
Factor with a box
Solve problems with polynomials