Page 489 - Algebra 1

LESSON Factoring Trinomials: x2 + bx + c 72
Warm Up
1. Vocabulary A polynomial with two terms is a . (53)
Simplify.
2. (5x+3)(2x-4)
(58)
3. (5x - 6)2 (60)
4. (x + 1) (x2 + 3) (58)
New Concepts The polynomial x2 + bx + c is a trinomial. Like numbers, some trinomials can be factored. One way to learn how to factor a trinomial is to model the
Math Reasoning
Generalize Why is
x2 + bx + c classified as a trinomial?
Online Connection www.SaxonMathResources.com
terms of a trinomial with algebra tiles.
Exploration Representing Trinomials with Algebra Tiles The following tiles represent terms in the trinomial x2 + 3x + 2.
x +1 +1 +1
x xxx+1+1
+1 +1
The tiles that represent some trinomials can be placed side by side to form rectangles. The tiles can be arranged to form a rectangle that has the dimensions (x + 2) and (x + 1).
(x + 2)
x +1 +1
The area of the rectangle formed by the tiles can be represented as
(x + 2)(x + 1). By simplifying the product, the result will be the trinomial x2 +3x+2.Thebinomialsx+2andx+1arethefactorsof x2 +3x+2.
a. Model Draw the tiles that represent the trinomial x2 + 4x + 3.
b. Arrange the tiles into a rectangle.
c. Analyze What are the dimensions of the rectangle?
d. Formulate Use the dimensions of the rectangle to calculate the area of the rectangle.
e. Analyze What are the factors of x2 + 4x + 3?
x
+1
(x + 1)
474 Saxon Algebra 1