Page 731 - Basic College Mathematics with Early Integers

A PPEND I X B .1 I ADDING AND SUBTRACTING POLYNOMIALS 707

Example 7 Subtract: 18x - 4x + 12 - 110x + 42 PRACTICE 7
2
2
Subtract:
Solution: 111x + 7x + 22 - 115x + 4x2
2
2
Add the
2 2 2 2
18x - 4x + 12 - 110x + 42 = 18x - 4x + 12 + 1-10x - 42 opposite of
2
10x + . 4
2
2
= 8x - 10x - 4x + 1 - 4 Group like terms.
2
=-2x - 4x - 3
Work Practice 7
Example 8 Subtract 1-6z - 2z + 132 from 14z - 20z2. PRACTICE 8
2
2
2
Subtract 13x - 12x2 from
Solution: Be careful when arranging the polynomials in this example. 1-4x + 20x + 172.
2
2 2 2 2
14z - 20z2 - 1-6z - 2z + 132 = 14z - 20z2 + 16z + 2z - 132
2
2
= 4z + 6z - 20z + 2z - 13 Group like
terms.
2
= 10z - 18z - 13
Work Practice 8
Concept Check Find and explain the error in the following subtraction.
2 2
13x + 42 - 1x - 3x2
2 2
= 13x + 42 + 1-x - 3x2
2
2
= 3x - x - 3x + 4
2
= 2x - 3x + 4
Just as with adding polynomials, we can subtract polynomials using a vertical for-
mat. Let’s subtract the polynomials in Example 8 using a vertical format.
Example 9 Subtract 1-6z - 2z + 132 from 14z - 20z2. Use a vertical PRACTICE 9
2
2
2
format. Subtract 13x - 12x2 from
2
1-4x + 20x + 172. Use a
Solution: Line up like terms underneath one another.
vertical format.
2
4z - 20z 4z - 20z
2
2 2
-1-6z - 2z + 132 +6z + 2z - 13
2
10z - 18z - 13
Work Practice 9
Objective Evaluating Polynomials
Polynomials have different values depending on the replacement values for the
variables.
PRACTICE 10
Example 10 Find the value of the polynomial 3t - 2t + 5 when t = 1. Find the value of the polyno-
3
2
3
mial 2y + y - 6 when y = 3.
Solution: Replace t with 1 and simplify.
3
3
3t - 2t + 5 = 3112 - 2112 + 5 Let t = 1. Answers
2
7. -4x + 3x + 2
= 3112 - 2 + 5 112 = 1. 8. -7x + 32x + 17
3
2
2
= 3 - 2 + 5 9. -7x + 32x + 17 10. 57
= 6
Concept Check Answer
3
The value of 3t - 2t + 5 when t = 1 is 6. 2 2
13x + 42 - 1x - 3x2
2
2
Work Practice 10 = 13x + 42 + 1-x + 3x2
2
2
= 3x - x + 3x + 4
2
= 2x + 3x + 4