8.5 Adding and Subtracting 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.

Can you write an equation for the total

toys (T) sold?

3 2

3 2

V 0.5t 0.5t 1.4t 3.6

R 0.5t 1.9t 3t 19

=- + + +

= - + +

Add Polynomials

To add polynomials, group the LIKE TERMS

LIKE TERMS are variables that have the SAME LETTER and the SAME POWER.

Add polynomials – METHOD 1

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

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

=-4x2 - 2x + 3

Add polynomials – METHOD 2

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

-4x2 - 2x + 3

3x2 - 4x + 8

(+) -7x2 + 2x - 5

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.

GI VEN: 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.

Can you write an equation for the total

toys (T) sold?

3 2

3 2

V 0.5t 0.5t 1.4t 3.6

R 0.5t 1.9t 3t 19

=- + + +

= - + +

Warm up…

3 2

3 2

Given: V 0.5t 0.5t 1.4t 3.6

R 0.5t 1.9t 3t 19

=- + + +

= - + +

3 2

3 2

T 0.5t 0.5t 1.4t 3.6

0.5t 1.9t 3 t 19

= - + + +

+ - + +

T V R= +

2 1.4t 4.4t 22.6- + +

2 T 1.4t 4.4t 22.6=- + +

Homework

P441:13-31oddNotes 8.5