5 Minute Check Simplify each expression. Complete in your notes. 1. (-3x - 2) - (7x + 9) 2. (-2x - 1) - (x - 7) 3. (9x + 5) - (6x - 8) 4. (-8x + 1) - (8x.

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Presentation transcript:

5 Minute Check Simplify each expression. Complete in your notes. 1. (-3x - 2) - (7x + 9) 2. (-2x - 1) - (x - 7) 3. (9x + 5) - (6x - 8) 4. (-8x + 1) - (8x - 1)

5 Minute Check Simplify each expression. Complete in your notes. 1. (-3x - 2) - (7x + 9)

5 Minute Check Simplify each expression. Complete in your notes. 1. (-3x - 2) - (7x + 9) -3x x x - 11

5 Minute Check Simplify each expression. Complete in your notes. 2. (-2x - 1) - (x - 7)

5 Minute Check Simplify each expression. Complete in your notes. 2. (-2x - 1) - (x - 7) -2x x x + 6

5 Minute Check Simplify each expression. Complete in your notes. 3. (9x + 5) - (6x - 8)

5 Minute Check Simplify each expression. Complete in your notes. 3. (9x + 5) - (6x - 8) 9x x + 8 3x + 13

5 Minute Check Simplify each expression. Complete in your notes. 4. (-8x + 1) - (8x - 1)

5 Minute Check Simplify each expression. Complete in your notes. 4. (-8x + 1) - (8x - 1) -8x x x + 2

Monday, May 18 Lesson Factor Linear Expressions

Objective: To use properties of mathematics to factor linear expressions.

Factor Linear Expressions A monomial is a number, a variable, or a product of a number and one or more variables. Monomials; 25, x, 25x Not Monomials: x + 25, 25x + 100

Factor Linear Expressions To factor a number means to write it as a product of its prime factors. 36; 2 · 2 · 3 · 3

Factor Linear Expressions A linear algebraic expression can be factored using the same method you would use to factor a number.

Factor Linear Expressions Factor the expression x How to Factor Monomials. (Method 1) Step 1 – Write both monomials as prime factors.

Factor Linear Expressions Factor the expression x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x How to Factor Monomials. Step 1 – Write both monomials as prime factors.

Factor Linear Expressions Factor the expression x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x How to Factor Monomials. Step 2 – Circle the common factors.

Factor Linear Expressions Factor the expression x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x How to Factor Monomials. Step 2 – Circle the common factors.

Factor Linear Expressions Factor the expression x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x How to Factor Monomials. Step 3 – Find the GCF by multiplying the common factors for one number.

Factor Linear Expressions Factor the expression x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x GCF = 2 · 3 = 6 How to Factor Monomials. Step 3 – Find the GCF by multiplying the common factors for one number.

Factor Linear Expressions Factor the expression x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x GCF = 2 · 3 = 6 How to Factor Monomials. Step 4 – Rewrite the expression with the GCF outside the parenthesis. 3 0: 2 · 3 · 5 · x

Factor Linear Expressions Factor the expression x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x GCF = 2 · 3 = 6 6(2 + 5x) How to Factor Monomials. Step 4 – Rewrite the expression with the GCF outside the parenthesis.

Factor Linear Expressions Factor the expression x Step 1 – ?

Factor Linear Expressions Factor the expression x 8 = 2 · 2 · 2 12x = 2 · 2 · 3 · x Step 2 – ?

Factor Linear Expressions Factor the expression x 8 = 2 · 2 · 2 12x = 2 · 2 · 3 · x Step 3 –

Factor Linear Expressions Factor the expression x 8 = 2 · 2 · 2 12x = 2 · 2 · 3 · x The GCF is 2 · 2, or 4 Step 4 –

Factor Linear Expressions Factor the expression x 8 = 2 · 2 · 2 12x = 2 · 2 · 3 · x The GCF is 2 · 2, or 4 4(2 + 3x)

Factor Linear Expressions Factor the expression. 18a + 20ab How to Factor Monomials. (Method 2) Step 1 – Factor out any common variables.

Factor Linear Expressions Factor the expression. 18a + 20ab a( b) How to Factor Monomials. (Method 2) Step 1 – Factor out any common variables.

Factor Linear Expressions Factor the expression. 18a + 20ab a( b) How to Factor Monomials. (Method 2) Step 2 – Factor out 2, if possible, and keep factoring until you can’t.

Factor Linear Expressions Factor the expression. 18a + 20ab a( b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 2 – Factor out 2, if possible, and keep factoring until you can’t.

Factor Linear Expressions Factor the expression. 18a + 20ab a( b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 3 – Factor out 3, if possible, and keep factoring until you can’t.

Factor Linear Expressions Factor the expression. 18a + 20ab a( b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 3 – Factor out 3, if possible, and keep factoring until you can’t.

Factor Linear Expressions Factor the expression. 18a + 20ab a( b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 4 – Factor out any remaining prime numbers, if possible.

Factor Linear Expressions Factor the expression. 18a + 20ab a( b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 4 – Factor out any remaining prime numbers, if possible.

Factor Linear Expressions Factor the expression c Step 1 - ? (Method 2)

Factor Linear Expressions Factor the expression c Step 2 - ? (Method 2)

Factor Linear Expressions Factor the expression c 2(6 + 14c) 4(3 + 7c) Step 3 - ? (Method 2)

Factor Linear Expressions Factor the expression c 2(6 + 14c) 4(3 + 7c) Step 4 - ? (Method 2)

Factor Linear Expressions Factor the expression c 2(6 + 14c) 4(3 + 7c)

Factor Linear Expressions Factor the expression. 25x + 15xy Do this on your own.

Factor Linear Expressions Factor the expression. Method 1 25x + 15xy 25x = 5 · 5 · x 15xy = 3 · 5 · x · y The GCF is 5 · x, or 5x 5x (5 + 3y)

Factor Linear Expressions Factor the expression. Method 2 25x + 15xy x( y) 5x (5 + 3y)

Factor Linear Expressions Factor the expression. 42mn + 14n Do this on your own.

Factor Linear Expressions Factor the expression. Method 1 42mn + 14n 42mn = 2 · 3 · 7 · m · n 14n = 2 · 7 · n The GCF is 2 · 7 · n, or 14n 14n(3m + 1)

Factor Linear Expressions Factor the expression. Method 2 42mn + 14n n(42m + 14) 2n(21m + 7) 14n(3m + 1)

Factor Linear Expressions Factor the expression. 3x + 9

Factor Linear Expressions Factor the expression. Method 1 3x + 9 3x = 3 · x 9 = 3 · 3 The GCF is 3 3(x + 3)

Factor Linear Expressions Factor the expression. Method 2 3x + 9 3(x + 3)

Factor Linear Expressions Factor the expression. 12x + 7y

Factor Linear Expressions Factor the expression. 12x + 7y 12x = 2 · 2 · 3 · x 7y = 7 · y The are no common factors, the expression cannot be factored.

Factor Linear Expressions Factor the expression. 4x - 28

Factor Linear Expressions Factor the expression. Method 1 4x x = 2 · 2 · x 28 = 2 · 2 · 7 The GCF is 4 4(x - 7)

Factor Linear Expressions Factor the expression. Method 2 4x (2x – 14) 4(x - 7)

Factor Linear Expressions Factor the expression. 3x + 33y

Factor Linear Expressions Factor the expression. Method 1 3x + 33y 3x = 3 · x 33y = 3 · 11 · y The GCF is 3 3(x + 11y)

Factor Linear Expressions Factor the expression. Method 2 3x + 33y 3(x + 11y)

Factor Linear Expressions Factor the expression. 4x + 35

Factor Linear Expressions Factor the expression. 4x x = 2 · 2 · x 35 = 5 · 7 There is no GCF and cannot be factored.

Factor Linear Expressions Factor the expression. 32x + 18

Factor Linear Expressions Factor the expression. Method 1 32x x = 2 · 2 · 2 · 2 · 2 · x 18 = 2 · 3 · 3 The GCF is 2 2(16x + 9)

Factor Linear Expressions Factor the expression. Method 2 32x (16x + 9)

Factor Linear Expressions Factor the expression. 27s – 54st

Factor Linear Expressions Factor the expression. Method 1 27s – 54st 27s = 3 · 3 · 3 · s 54st = 2 · 3 · 3 · 3 · s · t The GCF is 27s 27s(1 – 2t)

Factor Linear Expressions Factor the expression. Method 2 27s – 54st s(27 – 54t) 3s(9 – 18t) 9s(3 – 6t) 27s(1 – 2t)

Factor Linear Expressions Factor the expression. 18cd + 30d

Factor Linear Expressions Factor the expression. Method 1 18cd + 30d 18cd = 2 · 3 · 3 · c · d 30d = 2 · 3 · 5 · d The GCF is 6d 6d(3c + 5)

Factor Linear Expressions Factor the expression. Method 2 18cd + 30d d(18c + 30) 2d(9c + 15) 6d(3c + 5)

Factor Linear Expressions Factor the expression. 36x + 24

Factor Linear Expressions Factor the expression. Method 1 36x x = 2 · 2 · 3 · 3 · x 24 = 2 · 2 · 2 · 3 The GCF is 12 12(3x + 2)

Factor Linear Expressions Factor the expression. Method 2 36x (18x + 12) 4(9x + 6) 12(3x + 2)

Factor Linear Expressions Factor the expression. 4x + 9

Factor Linear Expressions Factor the expression. 4x + 9 x = 2 · 2 · x 9 = 3 · 3 There is no GCF and cannot be factored.

Factor Linear Expressions Factor the expression. 14x – 16y

Factor Linear Expressions Factor the expression. Method 1 14x – 16y 14x = 2 · 7 · x 16y = 2 · 2 · 2 · 2 · y The GCF is 2. 2(7x – 8y)

Factor Linear Expressions Factor the expression. Method 2 14x – 16y 2(7x – 8y)

Factor Linear Expressions Agenda Notes Homework – Homework Practice due by the end of the period. Circle all answers and show all work with either method. Chapter 7.5 Test -Wednesday, May 20