Concept Byte: Using Models to Factor

Use With Lesson 8-5

ACTIVITY

You can sometimes write a trinomial as the product of two binomial factors. You can use algebra tiles to find the factors by arranging all of the tiles to form a rectangle. The lengths of the sides of the rectangle are the factors of the trinomial.

ACTIVITY

Write x 2 + 7 x + 12 bold italic x squared , plus 7 bold italic x plus 12  as the product of two binomial factors.

Model of polynomial

Use the tiles to form a rectangle.

First try:	Second try:	Third try:
There are six tiles left over.	There is one tile too few.	Correct! There is the exact number of tiles needed. x 2 + 7 x + 12 = ( x + 3 ) ( x + 4 ) x squared , plus 7 x plus 12 equals open x plus 3 close open x plus 4 close

Exercises

Use algebra tiles to find binomial factors of each trinomial.

1. x 2 + 4 x + 4 x squared , plus 4 x plus 4
2. x 2 + 5 x + 6 x squared , plus 5 x plus 6
3. x 2 + 10 x + 9 x squared , plus 10 x plus 9
4. x 2 + 7 x + 10 x squared , plus 7 x plus 10
5. x 2 + 9 x + 14 x squared , plus 9 x plus 14
6. x 2 + 8 x + 16 x squared , plus 8 x plus 16
7. Reasoning Explain why you cannot use algebra tiles to represent the trinomial x 2 + 2 x + 3 x squared , plus 2 x plus 3  as a rectangle.

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