9-2 Multiplying and Factoring Monomials

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Presentation transcript:

9-2 Multiplying and Factoring Monomials

Multiplying by a Monomial We have already multiplied a number by a polynomial. 5(3x2 + 6x – 7) Distribute! 15x2

Multiplying by a Monomial We have already multiplied a number by a polynomial. 5(3x2 + 6x – 7) Distribute! 15x2 + 30x

Multiplying by a Monomial We have already multiplied a number by a polynomial. 5(3x2 + 6x – 7) Distribute! 15x2 + 30x – 35 Nothing changes just because we added variables.

Multiplying by a Monomial We have already multiplied a number by a polynomial. 5(3x2 + 6x – 7) Distribute! 15x2 + 30x – 35 Nothing changes just because we added variables. 3x2(2x2 – 5x + 1)

Multiplying by a Monomial We have already multiplied a number by a polynomial. 5(3x2 + 6x – 7) Distribute! 15x2 + 30x – 35 Nothing changes just because we added variables. 3x2(2x2 – 5x + 1) 6x4

Multiplying by a Monomial We have already multiplied a number by a polynomial. 5(3x2 + 6x – 7) Distribute! 15x2 + 30x – 35 Nothing changes just because we added variables. 3x2(2x2 – 5x + 1) 6x4 – 15x3

Multiplying by a Monomial We have already multiplied a number by a polynomial. 5(3x2 + 6x – 7) Distribute! 15x2 + 30x – 35 Nothing changes just because we added variables. 3x2(2x2 – 5x + 1) 6x4 – 15x3 + 3x2

Finding Your “Good Close Friend” When trying to simplify a polynomial, finding your GCF (greatest common factor) is your first line of defense. 10x4 – 5x2 +15 What is “common” to all 3 terms? 5 So, we take out the common thing. 5(

Finding Your “Good Close Friend” When trying to simplify a polynomial, finding your GCF (greatest common factor) is your first line of defense. 10x4 – 5x2 +15 What is “common” to all 3 terms? 5 So, we take out the common thing. 5(2x4

Finding Your “Good Close Friend” When trying to simplify a polynomial, finding your GCF (greatest common factor) is your first line of defense. 10x4 – 5x2 +15 What is “common” to all 3 terms? 5 So, we take out the common thing. 5(2x4 – x2

Finding Your “Good Close Friend” When trying to simplify a polynomial, finding your GCF (greatest common factor) is your first line of defense. 10x4 – 5x2 +15 What is “common” to all 3 terms? 5 So, we take out the common thing. 5(2x4 – x2 + 3) This is called the “factored form”

Finding Your “Good Close Friend” 3x4 + 9x2 +12x What is “common” to all 3 terms? 3x So, we take out the common thing. 3x(

Finding Your “Good Close Friend” 3x4 + 9x2 +12x What is “common” to all 3 terms? 3x So, we take out the common thing. 3x(x3

Finding Your “Good Close Friend” 3x4 + 9x2 +12x What is “common” to all 3 terms? 3x So, we take out the common thing. 3x(x3 + 3x

Finding Your “Good Close Friend” 3x4 + 9x2 +12x What is “common” to all 3 terms? 3x So, we take out the common thing. 3x(x3 + 3x +4)

Example #1 Multiply: 3x2(-8x + 2)

Example #1 Multiply: 3x2(-8x + 2) = -24x3

Example #1 Multiply: 3x2(-8x + 2) = -24x3 + 6x2

Example #2 Factor: 4x3 – 2x2

Example #2 Factor: 4x3 – 2x2 = 2x2(

Example #2 Factor: 4x3 – 2x2 = 2x2(2x

Example #2 Factor: 4x3 – 2x2 = 2x2(2x – 1)

Today’s Assignment P. 501 #1-31 odds