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

Model the polynomial with algebra tiles

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

Factor the polynomial

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 ?

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

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.

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

To find the perimeter, add the sides w The perimeter of the poster in terms of the width is 6w + 2 inches 2w+1 2w+1 w

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

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

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?

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