# 8.5 Adding and Subtracting Polynomials

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Polynomials
Warm up…
   From 1996 to 1999, the amount of sales
(in billions of dollars) of video games V
and traditional toys R in the US can be
modeled by the following equations where
t is the number of years since 1996.
V = - 0.5t3 + 0.5t2 + 1.4t + 3.6
R = 0.5t3 - 1.9t2 + 3t + 19
Can you write an equation for the total
toys (T) sold?

 To add polynomials, group the LIKE
TERMS
 LIKE TERMS are variables that have the
SAME LETTER and the SAME POWER.

(3x2 - 4x + 8) + (2x - 7x2 - 5)

=(3x2 - 7x2 ) + ( -4x + 2x) + (+8 - 5)

=-4x2 - 2x + 3

(3x2-4x+8) + (2x-7x2-5)

3x2 - 4x + 8
(+) -7x2 + 2x - 5
-4x2 - 2x + 3
Subtract polynomials – METHOD 1

(3x2 + 13x3 + 5x) - (7x + 4x3)

=(3x2 + 13x3 + 5x) + (-7x - 4x3)
= (13x3 - 4x3) + 3x2 + (5x -7x)
= 9x3 + 3x2 - 2x
Subtract polynomials – METHOD 2

(3x2 + 13x3 + 5x) - (7x + 4x3)

=(3x2 + 13x3 + 5x) + (-7x - 4x3)

13x3 + 3x2 + 5x
(+) - 4x3     - 7x

9x3 + 3x2 - 2x
Subtract Polynomials
The total number of public school teachers consists
of two groups, elementary and secondary. From
1985 through 1988, the number (in thousands) of
secondary teachers and the total teachers could be
modeled by the following equations, where n is the
number of years since 1985.

S = 11n + 942    (S=secondary teachers)
T = 44n + 2216 (T=total teachers)
Subtract Polynomials
Find an equation that models the number of
elementary teachers, E, for the same time period.

GIVEN: S = 11n + 942     (S=secondary teachers)
T = 44n + 2216 (T=total teachers)

E=T-S:   E = (44n + 2216) - (11n + 942)
E = (44n + 2216) + (- 11n - 942)
E = (44n - 11n) + (2216 - 942)
E = 33n + 1274
Subtract Polynomials
Predict the number of elementary teachers in the
year 2010.
Given : E = 33n + 1274
n = number of years since 1985
n = 2010 - 1985 = 25
E = 33(25) + 1274
E = 825 + 1274 = 2099 thousand
E = 2,099,000
Warm up…
   From 1996 to 1999, the amount of sales
(in billions of dollars) of video games and
traditional toys can be modeled by the
following equations where t is the number
of years since 1996.
V = - 0.5t3 + 0.5t2 + 1.4t + 3.6
R = 0.5t3 - 1.9t2 + 3t + 19
Can you write an equation for the total
toys (T) sold?
Warm up…
Given :   V = - 0.5t3 + 0.5t2 + 1.4t + 3.6
3        2
R = 0.5t - 1.9t + 3t + 19

T = V+ R
T=       - 0.5t3 + 0.5t2 + 1.4t + 3.6
+    0.5t3 - 1.9t2     + 3 t + 19

- 1.4t2     + 4.4t + 22.6

T = - 1.4t2 + 4.4t + 22.6
Homework

 P441:13-31odd
 Notes 8.5

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