7.5 – Adding & Subtracting Polynomials. “Combining Like Terms” -

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Presentation transcript:

7.5 – Adding & Subtracting Polynomials

“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 (3x 2 – 4x + 8) + (2x – 7x 2 – 5).

“Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!! Ex. 1 Find (3x 2 – 4x + 8) + (2x – 7x 2 – 5). (3x 2 – 4x + 8) + (2x – 7x 2 – 5)

“Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!! Ex. 1 Find (3x 2 – 4x + 8) + (2x – 7x 2 – 5). (3x 2 – 4x + 8) + (2x – 7x 2 – 5) 3x 2 – 4x x – 7x 2 – 5

“Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!! Ex. 1 Find (3x 2 – 4x + 8) + (2x – 7x 2 – 5). (3x 2 – 4x + 8) + (2x – 7x 2 – 5) 3x 2 – 4x x – 7x 2 – 5

“Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!! Ex. 1 Find (3x 2 – 4x + 8) + (2x – 7x 2 – 5). (3x 2 – 4x + 8) + (2x – 7x 2 – 5) 3x 2 – 4x x – 7x 2 – 5 3x 2 – 7x 2

“Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!! Ex. 1 Find (3x 2 – 4x + 8) + (2x – 7x 2 – 5). (3x 2 – 4x + 8) + (2x – 7x 2 – 5) 3x 2 – 4x x – 7x 2 – 5 3x 2 – 7x 2

“Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!! Ex. 1 Find (3x 2 – 4x + 8) + (2x – 7x 2 – 5). (3x 2 – 4x + 8) + (2x – 7x 2 – 5) 3x 2 – 4x x – 7x 2 – 5 3x 2 – 7x 2 – 4x + 2x

“Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!! Ex. 1 Find (3x 2 – 4x + 8) + (2x – 7x 2 – 5). (3x 2 – 4x + 8) + (2x – 7x 2 – 5) 3x 2 – 4x x – 7x 2 – 5 3x 2 – 7x 2 – 4x + 2x

“Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!! Ex. 1 Find (3x 2 – 4x + 8) + (2x – 7x 2 – 5). (3x 2 – 4x + 8) + (2x – 7x 2 – 5) 3x 2 – 4x x – 7x 2 – 5 3x 2 – 7x 2 – 4x + 2x + 8 – 5

“Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!! Ex. 1 Find (3x 2 – 4x + 8) + (2x – 7x 2 – 5). (3x 2 – 4x + 8) + (2x – 7x 2 – 5) 3x 2 – 4x x – 7x 2 – 5 3x 2 – 7x 2 – 4x + 2x + 8 – 5 – 4x 2 – 2x + 3

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

3n n 3 + 5n – 7n

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

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

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

Ex. 2 Find (3n n 3 + 5n) – (7n + 4n 3 ). 3n n 3 + 5n – 7n – 4n 3 13n 3 – 4n 3 + 3n 2 + 5n – 7n 9n 3 + 3n 2 – 2n

Ex. 2 Find (3n n 3 + 5n) – (7n + 4n 3 ). 3n n 3 + 5n – 7n – 4n 3 13n 3 – 4n 3 + 3n 2 + 5n – 7n 9n 3 + 3n 2 – 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 F = 1247n + 126,971M = 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

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, n + 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, n + 120,741 T = 1247n n + 126, ,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, n + 120,741 T = 1247n n + 126, ,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 + male T = F + M T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126, n + 120,741 T = 1247n n + 126, ,741 T = 2499n + 247,712 b. 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 + male T = F + M T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126, n + 120,741 T = 1247n n + 126, ,741 T = 2499n + 247,712 b. 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 + male T = F + M T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126, n + 120,741 T = 1247n n + 126, ,741 T = 2499n + 247,712 b. 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 + male T = F + M T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126, n + 120,741 T = 1247n n + 126, ,741 T = 2499n + 247,712 b. If this trend continues, what will the population of the United States Be in 2010? T = 2499n + 247,712 n = 2010 – 1990 = 20 T = 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 + male T = F + M T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126, n + 120,741 T = 1247n n + 126, ,741 T = 2499n + 247,712 b. If this trend continues, what will the population of the United States Be in 2010? T = 2499n + 247,712 n = 2010 – 1990 = 20 T = 2499(20) + 247,712 T = 297,692

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, n + 120,741 T = 1247n n + 126, ,741 T = 2499n + 247,712 b. If this trend continues, what will the population of the United States Be in 2010? T = 2499n + 247,712 n = 2010 – 1990 = 20 T = 2499(20) + 247,712 T = 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 + male T = F + M T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126, n + 120,741 T = 1247n n + 126, ,741 T = 2499n + 247,712 b. If this trend continues, what will the population of the United States Be in 2010? T = 2499n + 247,712 n = 2010 – 1990 = 20 T = 2499(20) + 247,712 T = 297,692 (thousand) T = 297,692,000