Page 90 - Math Course 2 (Book 1)

Polynomials

Mo. 3

Lesson 5 Method 2 Add horizontally.

2
2
(6x – 3x + 1) + (–x + x – 1) Write the
expression.
KEY CONCEPTS:
2
2
1. Add polynomials. = [6x + (–x )] + (–3x + x) + (1 – 1) Group like
terms.
2
= 5x – 2x Simplify.
MO. 3 - L5a
2
Answer The sum is 5x – 2x.
Adding Polynomials

2
2
2
2
Find (4x – 3y ) + (x + 4xy + y ).
Let’s Begin Method 1 Add vertically. Leave a space
because there is no
2
4x – 3y 2 other term like xy.
Adding Polynomials (+) x + 4xy + y 2
2
2

5x – 4xy – 2y 2
Examples
2
2
Answer The sum is 5x + 4xy –2y .
Find (9w – 4) + (w + 5).

Method 1 Add vertically. Real World Example

9w – 4 GEOMETRY
The length of a rectangle is 3x² + 2x – 5 units and
(+) w + 5 Align like terms. the width is 8x – 1 units. Find the perimeter.
10w + 1 Add.
P = 2ℓ + 2w Formula for the
perimeter of a
Method 2 Add horizontally
rectangle.
(9w – 4) + (w + 5) Associative and 2 Replace ℓ with
Commutative P = 2(3x + 2x – 5) + 2(8x – 1)
2
3x + 2x – 5 and w
= (9w + w) + (–4 + 5) Properties with 8x – 1.
2
= 10w + 1 P = 6x + 4x – 10 + 16x – 2 Distributive
Property.
Answer The sum is 10w + 1. P = 6x + (4x + 16x) + (–10 – 2) Group like terms.
2
2
P = 6x + 20x – 12 Simplify.
Find (6x² – 3x + 1) + (–x² + x – 1).
Find the perimeter of the rectangle if x = 3.
Method 1 Add vertically.
2
P = 6x + 20x – 12 Equation for the perimeter
2
2
6x – 3x + 1 P = 6(3) + 20(3) – 12 Replace x with 3.
2
(+) – x + x– 1 Align like terms P = 102 Simplify.
2
5x – 2x + 0 Add.
The perimeter of the rectangular
Answer
is 102 units when x = 3.
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