7.5 – Adding & Subtracting Polynomials

7.5 – Adding & Subtracting Polynomials

“Combining Like Terms” -

“Combining Like Terms” - ???

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).

(3x2 – 4x + 8) + (2x – 7x2 – 5)

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).

(3x2 – 4x + 8) + (2x – 7x2 – 5)

3x2 – 4x + 8 + 2x – 7x2 – 5

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).

(3x2 – 4x + 8) + (2x – 7x2 – 5)

3x2 – 4x + 8 + 2x – 7x2 – 5

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).

(3x2 – 4x + 8) + (2x – 7x2 – 5)

3x2 – 4x + 8 + 2x – 7x2 – 5

3x2 – 7x2

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).

(3x2 – 4x + 8) + (2x – 7x2 – 5)

3x2 – 4x + 8 + 2x – 7x2 – 5

3x2 – 7x2

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).

(3x2 – 4x + 8) + (2x – 7x2 – 5)

3x2 – 4x + 8 + 2x – 7x2 – 5

3x2 – 7x2 – 4x + 2x

“Combining Like Terms” - ???

- Only if have exact same variables with exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).

(3x2 – 4x + 8) + (2x – 7x2 – 5)

3x2 – 4x + 8 + 2x – 7x2 – 5

3x2 – 7x2 – 4x + 2x

“Combining Like Terms” - ???- Only if have exact same variables with

exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5). (3x2 – 4x + 8) + (2x – 7x2 – 5) 3x2 – 4x + 8 + 2x – 7x2 – 5 3x2 – 7x2 – 4x + 2x + 8 – 5

“Combining Like Terms” - ???- Only if have exact same variables with

exact same exponents on those variables!!!

Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5). (3x2 – 4x + 8) + (2x – 7x2 – 5) 3x2 – 4x + 8 + 2x – 7x2 – 5 3x2 – 7x2 – 4x + 2x + 8 – 5

– 4x2 – 2x + 3

Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).

Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).

Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).

3n2 + 13n3 + 5n – 7n

Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).

3n2 + 13n3 + 5n – 7n – 4n3

Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).

3n2 + 13n3 + 5n – 7n – 4n3

Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).

3n2 + 13n3 + 5n – 7n – 4n3

13n3 – 4n3 + 3n2 + 5n – 7n

Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).

3n2 + 13n3 + 5n – 7n – 4n3

13n3 – 4n3 + 3n2 + 5n – 7n 9n3 + 3n2 – 2n

Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).

3n2 + 13n3 + 5n – 7n – 4n3

13n3 – 4n3 + 3n2 + 5n – 7n 9n3 + 3n2 – 2n

Ex. 3

From 1990 through 1999, the female population F and the male population M of the United States (in thousands) are modeled by the following equations, where n is the number of years since 1990.

F = 1247n + 126,971 M = 1252n + 120,741

a. Find an equation that models the total population T in thousands of the United States for this time period.

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + male

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + male

T = F + M

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + male

T = F + M

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + male

T = F + M

T = (1247n + 126,971)

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + male

T = F + M

T = (1247n + 126,971)

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + male

T = F + M

T = (1247n + 126,971)+(1252n + 120,741)

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + male

T = F + M

T = (1247n + 126,971)+(1252n + 120,741)

T = 1247n + 126,971 + 1252n + 120,741

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + male

T = F + M

T = (1247n + 126,971)+(1252n + 120,741)

T = 1247n + 126,971 + 1252n + 120,741

T = 1247n + 1252n + 126,971 + 120,741

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + male

T = F + M

T = (1247n + 126,971)+(1252n + 120,741)

T = 1247n + 126,971 + 1252n + 120,741

T = 1247n + 1252n + 126,971 + 120,741

T = 2499n + 247,712

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + maleT = F + M

T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741

T = 2499n + 247,712b. If this trend continues, what will the

population of the United States Be in 2010?

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + maleT = F + M

T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741

T = 2499n + 247,712b. If this trend continues, what will the

population of the United States Be in 2010?T = 2499n + 247,712

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + maleT = F + M

T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741

T = 2499n + 247,712b. If this trend continues, what will the

population of the United States Be in 2010?T = 2499n + 247,712

n = 2010 – 1990 = 20

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + maleT = F + M

T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741

T = 2499n + 247,712b. If this trend continues, what will the population

of the United States Be in 2010?T = 2499n + 247,712

n = 2010 – 1990 = 20T = 2499(20) + 247,712

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + maleT = F + M

T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741

T = 2499n + 247,712b. If this trend continues, what will the population

of the United States Be in 2010?T = 2499n + 247,712

n = 2010 – 1990 = 20T = 2499(20) + 247,712T = 297,692

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + maleT = F + M

T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741

T = 2499n + 247,712b. If this trend continues, what will the population

of the United States Be in 2010?T = 2499n + 247,712

n = 2010 – 1990 = 20T = 2499(20) + 247,712T = 297,692 (thousand)

a. Find an equation that models the total population T in thousands of the United States for this time period.

T = female + maleT = F + M

T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741

T = 2499n + 247,712b. If this trend continues, what will the population

of the United States Be in 2010?T = 2499n + 247,712

n = 2010 – 1990 = 20T = 2499(20) + 247,712T = 297,692 (thousand)T = 297,692,000