Study Guide and Intervention
NAME
DATE
14-3
PERIOD
Study Guide and Intervention Subtracting Polynomials
Subtracting Polynomials Using Models
You can subtract polynomials using models. First, draw a model to represent the first polynomial. Then, remove the tiles that are represented by the second polynomial. Example
Subtract. Use models.
a. (6x + 5) - (3x + 3) Step 1 Model the polynomial 6x + 5. Step 2 To subtract 3x + 3, remove three x-tiles and three 1-tiles.
Y
Y
Y
Y
Y
Y
6x
+
1
1
1
1
+
1
5
Step 3 Write the polynomial for the remaining tiles. (6x + 5) - (3x + 3) = 3x + 2 b. x2 - 5x - 2 - (-x - 1) Step 1 Write the polynomial as the sum of terms. Then model the polynomial.
Y x2
2
+ -Y
-Y -Y -Y -Y + -1 -1
+
-5x
+
-2
Step 3 Write the polynomial for the remaining tiles. (x2 - 5x - 2) - (-x - 1) = x2 - 4x - 1
Exercises Subtract. Use models if needed. 1. (6x - 3) - (2x - 2)
2. (5x + 6) - (2x + 3)
3. (x2 + 6x - 5) - (3x - 2)
4. (x2 - 4x - 6) - (-3x - 2)
5. (x2 + 7x + 5) - (x2 + 4x + 2)
6. (2x2 - 4x - 3) - (x2 - 2x - 1)
Chapter 14
16
Glencoe Pre-Algebra
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Step 2 To subtract -x - 1, remove one negative x-tiles and one negative 1-tile.
NAME
14-3
DATE
PERIOD
Study Guide and Intervention
(continued)
Subtracting Polynomials Add Zero Pairs to Subtract Polynomials
When subtracting polynomials, you may need to add a zero pair to the model so that the subtraction can be performed. A zero pair is a positive tile and a negative tile of the same shape paired together. Example
Find (3x2 + 4x - 1) - (x2 - 3x).
Step 1 Write the polynomial as the sum of terms. Then model the polynomial.
Y
2
Y
2
Y
2
3x 2
+ Y +
Y
Y 4x
Y + -1 + -1
Step 2 Since there are no negative x-tiles to remove, add 3 zero pairs of x-tiles. Y
2
Y
2
Y
2
-Y Y -Y Y -Y Y
Y
Y
Y
Y
-1
Y
Y
Y
Y
-1
3 zero pairs
Y
2
Y
2
Y
2
-Y Y -Y Y -Y Y
Lesson 14-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Step 3 Remove 1 x2-tile and 3 negative x-tiles.
So, (3x2 + 4x - 1) - (x2 - 3x) = 2x2 + 7x - 1.
Exercises Subtract. Use models if needed. 1. (2x - 1) - (x + 3)
2. (2x + 1) - (x - 3)
3. (x2 + 4x + 2) - (-2x + 1)
4. (x2 + 2x - 3) - (-4x - 2)
5. (3x2 + 7x + 4) - (x2 + 3x - 4)
6. (4x2 - 4x - 3) - (x2 - 2x + 1)
7. (3x2 + x + 4) - (x2 + 2x - 2)
8. (2x2 + 3x - 3) - (x2 - 1x - 1)
Chapter 14
17
Glencoe Pre-Algebra
DATE
14-3
PERIOD
Study Guide and Intervention Subtracting Polynomials
Subtracting Polynomials Using Models
You can subtract polynomials using models. First, draw a model to represent the first polynomial. Then, remove the tiles that are represented by the second polynomial. Example
Subtract. Use models.
a. (6x + 5) - (3x + 3) Step 1 Model the polynomial 6x + 5. Step 2 To subtract 3x + 3, remove three x-tiles and three 1-tiles.
Y
Y
Y
Y
Y
Y
6x
+
1
1
1
1
+
1
5
Step 3 Write the polynomial for the remaining tiles. (6x + 5) - (3x + 3) = 3x + 2 b. x2 - 5x - 2 - (-x - 1) Step 1 Write the polynomial as the sum of terms. Then model the polynomial.
Y x2
2
+ -Y
-Y -Y -Y -Y + -1 -1
+
-5x
+
-2
Step 3 Write the polynomial for the remaining tiles. (x2 - 5x - 2) - (-x - 1) = x2 - 4x - 1
Exercises Subtract. Use models if needed. 1. (6x - 3) - (2x - 2)
2. (5x + 6) - (2x + 3)
3. (x2 + 6x - 5) - (3x - 2)
4. (x2 - 4x - 6) - (-3x - 2)
5. (x2 + 7x + 5) - (x2 + 4x + 2)
6. (2x2 - 4x - 3) - (x2 - 2x - 1)
Chapter 14
16
Glencoe Pre-Algebra
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Step 2 To subtract -x - 1, remove one negative x-tiles and one negative 1-tile.
NAME
14-3
DATE
PERIOD
Study Guide and Intervention
(continued)
Subtracting Polynomials Add Zero Pairs to Subtract Polynomials
When subtracting polynomials, you may need to add a zero pair to the model so that the subtraction can be performed. A zero pair is a positive tile and a negative tile of the same shape paired together. Example
Find (3x2 + 4x - 1) - (x2 - 3x).
Step 1 Write the polynomial as the sum of terms. Then model the polynomial.
Y
2
Y
2
Y
2
3x 2
+ Y +
Y
Y 4x
Y + -1 + -1
Step 2 Since there are no negative x-tiles to remove, add 3 zero pairs of x-tiles. Y
2
Y
2
Y
2
-Y Y -Y Y -Y Y
Y
Y
Y
Y
-1
Y
Y
Y
Y
-1
3 zero pairs
Y
2
Y
2
Y
2
-Y Y -Y Y -Y Y
Lesson 14-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Step 3 Remove 1 x2-tile and 3 negative x-tiles.
So, (3x2 + 4x - 1) - (x2 - 3x) = 2x2 + 7x - 1.
Exercises Subtract. Use models if needed. 1. (2x - 1) - (x + 3)
2. (2x + 1) - (x - 3)
3. (x2 + 4x + 2) - (-2x + 1)
4. (x2 + 2x - 3) - (-4x - 2)
5. (3x2 + 7x + 4) - (x2 + 3x - 4)
6. (4x2 - 4x - 3) - (x2 - 2x + 1)
7. (3x2 + x + 4) - (x2 + 2x - 2)
8. (2x2 + 3x - 3) - (x2 - 1x - 1)
Chapter 14
17
Glencoe Pre-Algebra
