Algebra 1 Common Core Student Edition, Grade 8-9

C oncept Byte

U se W i t h Lesson 11 - 3

® Common Core State Standards

DivifJinfl Pn lvn n m in k PreparesforA-APR.D.7 ...add,subtract,

LSI V IV III IfJ I W l jf I I v l I llU la multiply, and divide rational expressions.

Using Alg eb r a Tiles

MP 7

You can use algebra tiles to m odel polynom ial division.

Activity

What is (x2 + 4x + 3) -j- (x + 3)? Use algebra tiles.

Step 1 Use algebra tiles to m odel

the dividend, x2 + 4x + 3.

I J J J

Step 2 Use the x2-tile a n d th e 1-tiles to form

a figure w ith length x + 3, the divisor.

Step 3 Use th e rem aining tiles to

fill in th e rectangle.

x + 3

Since (x + l)(x + 3) = x 2 + 4x 4- 3, you can w rite (x2 + 4x + 3) f (x + 3) = x + 1.

Check Check your result by m ultiplying x + 1 an d x + 3. The p ro d u ct

should be th e dividend, x2 + 4x + 3.

(x + l)(x + 3) = (x)(x) + (x)(3) + (l)(x ) + (1)(3)

= x 2 + 3x + x + 3

= x 2 + 4x + 3

x + 1

Ex e r c i se s

Use algebra tiles to find each quotient. Check your result.

1. (x2 + 6x + 8) if (x + 4) 2. (x2 + 5x + 6) -t- (x + 2)

3. (x2 + 8x + 12) 4- (x + 6) 4. (x2 + 8x + 7) h- (x + 1)


4. Reasoning In Exercises 1-4, th e divisor is a factor of the dividend. How do you
   know? Can you use algebra tiles to rep resen t polynom ial division w h en th e divisor
   is not a factor of th e dividend? Explain.

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