Title: Algebra 1
Author: Mandy McDaniel
Last saved by: Glencoe Mathematics

Lesson 7-4

Example 1 Add Polynomials
Find (9 – 5a^2+ a) + (a^2 + 3a^3– 4a).
Method 1	Horizontal
(9 – 5a^2+ a) + (a^2 + 3a^3– 4a)
= 3a^3 + (-5a^2 + a^2) + [a + (-4a)] + 9	Group like terms.
= 3a^3 – 4a^2 – 3a  + 9	Add like terms.

Method 2	Vertical
            - 5a^2 +   a + 9	Notice that terms are in descending order
(+) 3a^3 +  a^2 – 4a       	with like terms aligned.
      3a^3 – 4a^2 – 3a + 9	

Example 2 Subtract Polynomials
Find (6x^2 – 17x^3 – 7) – (2x^2 – x^3 + x).
Method 1	Horizontal
Subtract 2x^2 – x^3 + x by adding its additive inverse.
(6x^2 – 17x^3 – 7) – (2x^2 – x^3 + x)
	= (6x^2 – 17x^3 – 7) + (-2x^2 + x^3 – x)	The additive inverse of 2x^2 – x^3 + x is -2x^2 + x^3 – x.
	= (-17x^3 + x^3) + [6x^2 + (-2x^2)] – x – 7	Group like terms.
	= -16x^3 + 4x^2 – x – 7	Add like terms.

Method 2	Vertical
Align like terms in columns and subtract by adding the additive inverse.	
     6x^2 – 17x^3        –  7	   6x^2 –  17x^3       –  7

Add the opposite.

(-) 2x^2 –     x^3 + x				(+) -2x^2  +     x^3  – x      	
					   4x^2  – 16x^3  – x – 7

Thus, (6x^2 – 17x^3 – 7) – (2x^2 – x^3 + x) = 4x^2 – 16x^3 – x – 7 or, arranged in descending order,
-16x^3 + 4x^2 – x – 7.

Example 3   Real-World EXAMPLE
The total number of students S enrolled in schools consists of two groups, public U and private R. From 1989 through 1999, the number (in thousands) of public school students and private school students could be modeled by the following equations, where n is the number of years since 1989.
S = 716.4n + 45,711
R = 82n + 5198
a.	Find an equation that models the number of students in public schools U for this time period.
Subtract the polynomial for R from the polynomial for S.

Add the opposite.

  Total	 716.4n +45,711	  716.4n + 45,711
- Private	(-)     82n +   5198		(+)    -82n –    5198
  Public		   634.4n + 40,513

An equation is U = 634.4n + 40,513.

b.	Use the equation to predict the number of public school students in the year 2010.
The year 2010 is 2010 – 1989 or 21 years after the year 1989. If this trend continues, the number of public school students in 2010 would be 634.4(21) + 40,513 thousand or about 53,835,400.