NAME: ______
UNIT 1 – RATIONAL EXPRESSIONS
Do Now: Factor
LESSON 1 – POLYNOMIALS
LESSON
1) Find the sum of
2) Find the difference of
3) Find the product of
4) Find the product of (7x – 2)(5x + 8)
5) Express as a trinomial (index card)
PRACTICE PROBLEMS
6) Find the sum of
7) Find the difference of (index card)
8) Find the product of
9) Find the product of
10) Find the product of
LESSON 1 HOMEWORK – Write each expression in simplest form.
1) Write index cards for page 1, ex. #5and page 2, ex. #7
2) Find the sum of
3) Find the difference of
4) Find the product of
5) Find the product of
6) Expand as a trinomial
Do Now: Factor
LESSON 2 – ABSOLUTE VALUE EQUATIONS
What is absolute value?
How do we solve absolute value equations? (index card)
1) Solve for all values of x: |x + 2| = 9
2) Solve for all values of a: |2a – 4| = 10
3) Solve for all values of n: |4n + 2| + 7 = 21 (index card)
4) Solve for all values of x: |2x + 6| + 10 = 2
PRACTICE PROBLEMS
5) Solve for all values of m: |2m – 3| = 2
6) Solve for all values of x: |3x| + 9 = 6
LESSON 2 HOMEWORK
1) Write index cards for page 4 steps, and page 5, ex. #3.
2) Solve for all values of x: |5x – 10| = 25
3) Solve for all values of y: |4y – 12| - 8 = 0
4) Solve for all values of a: |2a + 4| + 1 = -9
5) Solve for all values of n: |7 – n| + 2 = 12
Do Now: Factor
LESSON 3 – MORE ABSOLUTE VALUE EQUATIONS
1) Solve for all values of x: |2x – 3| + x = 9
2) Solve for all values of c: |c – 6| -2c = -3 (index card)
3) Solve for all values of m: |2m + 4| = m
PRACTICE PROBLEM
4) Solve for all values of x: |2x + 4| + x = 7
LESSON 3 HOMEWORK
1) Index Card – page 9, ex. #2
2) Solve for all values of y: |y – 1| = 3y
3) Solve for all values of k: |2k| + 3 = k
4) Solve for all values of x:
5) Solve for all values of y: |2y + 2| = 6y
Do Now: Factor 2x2 + 25x + 12
LESSON 4 – ABSOLUTE VALUE INEQUALITIES
Steps for Solving Absolute Value Inequalities (index card)
When is the shaded region connected? Also, when is the shaded region disconnected? (index card)
Ex. 1: Solve and graph on a number line: |x – 4| < 2
(1) 2 < x < 6 (3) -2 < x < 6
(2) x < 2 or x > 6 (4) x < -2 or x > 6
Ex. 2: Solve and graph on a number line: |2y + 6| 10
(1) -8 y 2 (3) y -8 or y 2
(2) 2 y 8 (4) y 2 or y 8
Ex. 3: Write the solution set as an inequality and graph on a number line: (index card)
|3m – 6| + 4 > 22
Ex. 4: Write the solution set as an inequality and graph on a number line:
|3 – x| < 4
PRACTICE PROBLEMS
Ex. 5: Solve and graph on a number line |4x + 8| 12
(1) x -5 or x -1 (3) -5 x -1
(2) x -5 or x 1 (4) -5 x 1
Ex. 6: Write the solution set as an inequality and graph on a number line
|| < 5
Ex. 7: Write the solution set as an inequality and graph on a number line
|x + 5| + 4 10
LESSON 4 HOMEWORK
1) Index Cards for steps on page 13, and exercise #3 on page 14
2) Write the solution set as an inequality and graph on a number line:
|5x + 2| 22
3) Write the solution set as an inequality and graph on a number line:
|2a| + 4 24
4) Solve and graph on a number line: || < 2
(1) -6 < n < 6 (3) n < 6
(2) n < -6 or n > 6 (4) n > -6
5) Write the solution set as an inequality and graph on a number line:
|4 – x| 7
6) Write the solution set as an inequality and graph on a number line:
|3n + 4| > 6
Do Now: Find the product in simplest form:
LESSON 5 – FACTORING REVIEW
A) How do we factor by GCF (single bubble)?
For each of the following, factor by GCF:
Ex. 1: (index card)
Ex. 2:
B) How do we factor a trinomial with a coefficient = 1 (double bubble)?
For each of the following, factor the trinomial:
Ex. 3: (index card)
Ex. 4:
C) How do we factor by DOTS (double bubble)? How do we recognize a DOTS exercise?
For each of the following, factor the binomial using DOTS:
Ex. 5: (index card)
Ex. 6:
PRACTICE PROBLEMS
D) Mixed up Factoring: Factor each of the following one-step polynomials
Ex. 10: Ex. 15:
Ex. 11: Ex. 16:
Ex. 12: 5t3 + 15t2 Ex. 17:
Ex. 13: Ex. 18:
Ex. 14: 6t5 – 20t2 Ex. 19: k2 – 5k + 6
LESSON 5 HOMEWORK
1) Index Cards for page 18, ex. #1, page 19, ex. #3 and 5
Factor each of the following:
2) 7) 4m3n2 + 6m4n
3) 8)
4) 9) u2 +25uv + 100v2
5) 225 – r2 10) 35k5 – 21k3
6) 11)
DO NOW: Review on subtracting polynomials with fractions
LESSON 6 – FACTORING TRINOMIALS WITH A COEFFICIENT OTHER THAN 1
(NO GCF)
How do we factor trinomials with coefficients other than 1? (index card)
Factor each of the following:
Ex. 1:
Ex. 2:
Ex. 3: (index card)
PRACTICE PROBLEMS
Ex. 4: 2x2 + 25x + 12
Ex. 5: 5t2 – 12t + 4
Ex. 6:
LESSON 6 HOMEWORK
1) Index Card – steps on page 22 and page 23, ex. #3
Factor each of the following.
2)
3) 7n2 – 16n + 4
4)
5)
Do Now: Solve for the solution set |x + 2| = 2
LESSON 7 – FACTORING COMPLETELY
How do we factor expressions that require multiple factoring techniques? (index card)
Ex. 1: 2x2 + 6x + 4
Ex. 2: 3y3 – 48y
Ex. 3: m3 – m2n – 30mn2
Ex. 4: 10x2 – 35x + 15 (index card)
Ex. 5: 50a2 – 8b2
PRACTICE PROBLEMS
Ex. 6: 28q2 - 175
Ex. 7: 6r2 – 32r + 10
Ex. 8: 10c2 + 20cd – 80d2
LESSON 7 HOMEWORK
1) Index Cards – steps on page 25, and page 26, ex. #4
Directions: Factor each expression completely.
Ex. 2: 5v2 – 40vw + 60w2
Ex. 3: 27m2 - 3
Ex. 4: k4 – 4k3 – 32k2
Ex. 5: 10a3 – 54a2 + 20a
Do Now: Graph the solution set on a number line:
4 > |x + 3|
LESSON 8 – SIMPLIFYING RATIONAL EXPRESSIONS
What are the steps for simplifying fractions? (index card)
When do we cancel out terms to -1? (index card)
Ex. 1:
Ex. 2:
Ex. 3: (index card)
Ex. 4: (index card)
PRACTICE PROBLEMS
Simplify the following fractions:
Ex. 5:
Ex. 6:
Ex. 7:
Ex. 8:
LESSON 8 HOMEWORK
1) Index Card – page 29 steps, page 30, ex #s 3 and 4,
Simplify the following fractions:
2)
3)
4)
5)
6)
7)
DO NOW: Solve for all values of y: y + 3 = |2y + 9|
LESSON 9 – MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS
How do we multiply rational expressions?
Ex. 1: (index card)
How do we divide rational expressions?
Ex. 2: (index card)
PRACTICE PROBLEMS
Ex. 3:
Ex. 4:
Ex. 5:
LESSON 9 HOMEWORK
1) Index Cards – page 34, ex. #1 and 2
Perform the indicated operations and write in simplest form.
1)
2)
3)
4)
DO NOW – Multiple choice, factor the following completely:
(1) (3)
(2) (4)
LESSON 10 – ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH COMMON DENOMINATORS
How do we add or subtraction rational expressions with a common denominator?
(index card)
Ex. 1:
Ex. 2:
Ex. 3:
Ex. 4: (index card)
Ex. 5:
LESSON 10 HOMEWORK
1) Index Cards – page 38 steps, and page 39, ex. #4
Find the sum or difference in simplest form:
2)
3)
4)
5)
DO NOW: Find the difference in simplest form:
LESSON 11 –ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH DIFFERENT DENOMINATORS
How do we add or subtract rational expressions that require the denominator to be factored? (index card)
Ex. 1:
Ex. 2: (index card)
Ex. 3:
PRACTICE PROBLEMS
Ex. 4:
Ex. 5:
Ex. 6:
LESSON 11 HOMEWORK
1) Index Cards – Steps page 41, and page 42, ex. #2
Perform the indicated operation and write the result in simplest form.
2)
3)
4)
DO NOW: (multiple choice) Find the difference in simplest form:
(1) (2) (3) (4)
LESSON 12 – COMPLEX FRACTIONS
How do we simplify complex fractions? (index card)
Ex. 1:
Ex. 2: (index card)
Ex. 3:
Ex. 4:
LESSON 12 HOMEWORK
1) Index Cards – Steps on page 45, and page 46, ex. #2
Express each rational expression in simplest form.
2)
3)
4)
5)
LESSON 13 – REVIEW FOR TEST
1) Study your index Cards!!!
2) Find each expression in simplest form:
a) Subtract with fractions
b) FOIL with fraction
3) Solve for the solution set |2n + 3| - n = 4
4) Write the solution set as an inequality and graph on a number line.
|4x + 1| 9
5) Perform each indicated operation in simplest form:
a)
b)
c)
6) Perform the indicated operation and simplify:
a)
b)
7) Write the expression in simplest form:
52