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# Factoring

Finding GCF, prime factorization, factoring monomials, binomials, trinomials, factoring using the distributive property, zero product property, applications.

by

Tweet## Tracy Cottrell

on 3 May 2011#### Transcript of Factoring

Factoring Factoring helps you reduce a number to its basic building blocks. A factor is an integer

which evenly divides a number. Factors of 10:

(Starting from 1, count to 10 and see if that number evenly divides into 10)

1, 2, 5, 10 Your turn!

Factors of 16:

A prime number is a whole number >1 whose only factors are 1 and itself. A composite number is a whole number >1 that is NOT prime. Factors of 7:

Is 7 prime?

Factors of 12:

Is 12 prime? You have been factoring all along!

6/4

(Factor out a 2 from the numerator and denomenator)

=3/2 Practice with factoring Factor 3 from 12:

3(__)=12

Check: 3(4)

Check: 3*4=12 Factor 4x from 32x :

4x (____)=32x

Check: 4x (8x)

Check: (4x )(8x)=32x When a whole number is expressed as a product of its prime factors, it is in its prime factorization. Find the GCF by using the prime factorization of

140 and 210

^ ^

2*70 10*21

| ^ ^ ^

2*2*35 2*5*3*7

| | ^ | | | |

2*2*5*7 2*5*3*7

GCF: 2*5*7= 70 Factor (12ac+21ad)+(8bc+14bd)

Can we factor the same expression from both groups?

3a(4c+7d)+2b(4c+7d)

Factor out (4c+7d) from both expressions.

(3a+2b)(4c+7d)

Check: Zero Product Property Using the Distributive Property with Factoring:

Distributive:

3(2a+b)=6a+3b

Factoring:

6a+3b=3(2a+b) The Zero Product Property states that if

a*b=0,

then a=0, b=0, or both a and b are zero. Set the expression = 0, then solve for x by factoring! Solve for x: Solve for b: (Hint: the degree gives you the number of answers!) x + 5x + 6=0 2 X 6 5 multiplied added ? ? _________________ _________________ _________________ _________________ _________________ _________________ x 6 2 2x 3x x + 5x +6 = 0 2 ? ? ? ? x + 5x +6 = 0 2 ____________ ____________ ____________ ____________ ____________ ____________ x 2x 3x 6 2 x 2 x 3 x + 5x + 6 = 0 2 ____________ ____________ ____________ ____________ ____________

____________ x 2x 3x 6 2 x x 2 3 (x+2)(x+3)=0 x+2=0 x+3=0 x= -2 x= -3 5b +34b = 7b 3 2 (Hint: the degree tells you the number of answers!) 5b +34b -7b=0 3 2 GCF? b(5b +34b -7)=0 2 Use what's in parenthesis to do X and box! b(5b +34b-7)=0 2 X (5)(-7)

-35 34 ? ? b(5b +34b-7)=0 2 __________ __________ __________ __________ __________ __________ 5b -7 35b -1b b 7 b(5b +34b -7) 2 __________ __________ __________ __________ __________ __________ 5b 35b -1b -7 b 7 5b 2 -1 b(5b +34b -7) 2 b(b+7)(5b-1)=0 b=0 b+7=0 5b-1=0 b=0, -7, 1 __ 5 b(5b +34b-7)=0 _______________ _______________ _______________ _______________ _______________ _______________ 2 5b 35b -1b -7 2 ? ? ? ? x + 5x +6 = 0 _________ _________ _________ _________ _________ _________ 2 x 2x 3x 6 2 x 2 ? ? 2 3 2 3 2 2 3 2

Full transcriptwhich evenly divides a number. Factors of 10:

(Starting from 1, count to 10 and see if that number evenly divides into 10)

1, 2, 5, 10 Your turn!

Factors of 16:

A prime number is a whole number >1 whose only factors are 1 and itself. A composite number is a whole number >1 that is NOT prime. Factors of 7:

Is 7 prime?

Factors of 12:

Is 12 prime? You have been factoring all along!

6/4

(Factor out a 2 from the numerator and denomenator)

=3/2 Practice with factoring Factor 3 from 12:

3(__)=12

Check: 3(4)

Check: 3*4=12 Factor 4x from 32x :

4x (____)=32x

Check: 4x (8x)

Check: (4x )(8x)=32x When a whole number is expressed as a product of its prime factors, it is in its prime factorization. Find the GCF by using the prime factorization of

140 and 210

^ ^

2*70 10*21

| ^ ^ ^

2*2*35 2*5*3*7

| | ^ | | | |

2*2*5*7 2*5*3*7

GCF: 2*5*7= 70 Factor (12ac+21ad)+(8bc+14bd)

Can we factor the same expression from both groups?

3a(4c+7d)+2b(4c+7d)

Factor out (4c+7d) from both expressions.

(3a+2b)(4c+7d)

Check: Zero Product Property Using the Distributive Property with Factoring:

Distributive:

3(2a+b)=6a+3b

Factoring:

6a+3b=3(2a+b) The Zero Product Property states that if

a*b=0,

then a=0, b=0, or both a and b are zero. Set the expression = 0, then solve for x by factoring! Solve for x: Solve for b: (Hint: the degree gives you the number of answers!) x + 5x + 6=0 2 X 6 5 multiplied added ? ? _________________ _________________ _________________ _________________ _________________ _________________ x 6 2 2x 3x x + 5x +6 = 0 2 ? ? ? ? x + 5x +6 = 0 2 ____________ ____________ ____________ ____________ ____________ ____________ x 2x 3x 6 2 x 2 x 3 x + 5x + 6 = 0 2 ____________ ____________ ____________ ____________ ____________

____________ x 2x 3x 6 2 x x 2 3 (x+2)(x+3)=0 x+2=0 x+3=0 x= -2 x= -3 5b +34b = 7b 3 2 (Hint: the degree tells you the number of answers!) 5b +34b -7b=0 3 2 GCF? b(5b +34b -7)=0 2 Use what's in parenthesis to do X and box! b(5b +34b-7)=0 2 X (5)(-7)

-35 34 ? ? b(5b +34b-7)=0 2 __________ __________ __________ __________ __________ __________ 5b -7 35b -1b b 7 b(5b +34b -7) 2 __________ __________ __________ __________ __________ __________ 5b 35b -1b -7 b 7 5b 2 -1 b(5b +34b -7) 2 b(b+7)(5b-1)=0 b=0 b+7=0 5b-1=0 b=0, -7, 1 __ 5 b(5b +34b-7)=0 _______________ _______________ _______________ _______________ _______________ _______________ 2 5b 35b -1b -7 2 ? ? ? ? x + 5x +6 = 0 _________ _________ _________ _________ _________ _________ 2 x 2x 3x 6 2 x 2 ? ? 2 3 2 3 2 2 3 2