Factoring using the Greatest Common Factor

Module 10 - Topic 1

FactorsA factor is a number that divides evenly into a number.

View this Cool Math website to review factors. There is only the 1 page to review.

Prime FactorizationA Prime number is divisible by 1 and itself.

Prime FactorizationA Prime number is divisible by 1 and itself.

Prime factorization are the prime factors that make up a number.

Prime FactorizationA Prime number is divisible by 1 and itself.

Prime factorization are the prime factors that make up a number.

Every number has a unique prime factorization.

Prime FactorizationA Prime number is divisible by 1 and itself.

Prime factorization are the prime factors that make up a number.

Every number has a unique prime factorization.

Such as the prime factorization of

A) 36 = 2 !2 ! 3 ! 3 or 22 ! 32

Prime FactorizationA Prime number is divisible by 1 and itself.

Prime factorization are the prime factors that make up a number.

Every number has a unique prime factorization.

Such as the prime factorization of

A)

B)

36 = 2 !2 ! 3 ! 3 or 22 ! 32

105 = 3 !5 ! 7

Prime FactorizationA Prime number is divisible by 1 and itself.

Prime factorization are the prime factors that make up a number.

Every number has a unique prime factorization.

Such as the prime factorization of

A)

B)

If you do not remember how to find the prime factorization of a number, Purple Math will help you review Prime Factorization here.

36 = 2 !2 ! 3 ! 3 or 22 ! 32

105 = 3 !5 ! 7

Finding & Factor GCF of a PolynomialView this 5 minute Prentice Hall video to learn how to find the GCF of a Polynomial.

Finding & Factor GCF of a PolynomialView this 5 minute Prentice Hall video to learn how to find the GCF of a Polynomial.

Now view this Cool Math website to learn how to factor the GCF from a polynomial.

There are 4 pages to review.

Be sure to do the Try It and Your Turn problems in your notebook. Check your answers on the following slides.

Factor:Page 2 Try It2x2 ! 4x

Factor:

= 2x ! x " 2x !2

Page 2 Try It2x2 ! 4x

Factor:

= 2x ! x " 2x !2

Page 2 Try It2x2 ! 4x

Factor:

= 2x ! x " 2x !2

= 2x x ! 2( )

Page 2 Try It2x2 ! 4x

Factor:

= 2x ! x " 2x !2

= 2x x ! 2( )

Page 2 Try It2x2 ! 4x

Factor:

Page 2 Try It

7x +14x2

Factor:

= 7x !1+ 7x !2x

Page 2 Try It

7x +14x2

Factor:

= 7x !1+ 7x !2x

Page 2 Try It

7x +14x2

Factor:

= 7x !1+ 7x !2x

= 7x 1+ 2x( )

Page 2 Try It

7x +14x2

Factor:

= 7x !1+ 7x !2x

= 7x 1+ 2x( )

Page 2 Try It

7x +14x2

Factor:15a2b4 ! 5ab3 + 20a3b3 +10a5b7

Page 4 Your Turn

Factor:15a2b4 ! 5ab3 + 20a3b3 +10a5b7

= 5ab3 ! 3ab " 5ab3 !1+ 5ab3 ! 4a2 + 5ab3 !2a4b4

Page 4 Your Turn

Factor:15a2b4 ! 5ab3 + 20a3b3 +10a5b7

= 5ab3 ! 3ab " 5ab3 !1+ 5ab3 ! 4a2 + 5ab3 !2a4b4

Page 4 Your Turn

Factor:15a2b4 ! 5ab3 + 20a3b3 +10a5b7

= 5ab3 ! 3ab " 5ab3 !1+ 5ab3 ! 4a2 + 5ab3 !2a4b4

= 5ab3 3ab !1+ 4a2 + 2a4b4( )

Page 4 Your Turn

Factor:6x4y3 + 2x2y2 ! 8x5y6

Page 4 Your Turn

Factor:6x4y3 + 2x2y2 ! 8x5y6

= 2x2y2 ! 3x2y + 2x2y2 !1" 2x2y2 ! 4x3y4

Page 4 Your Turn

Factor:6x4y3 + 2x2y2 ! 8x5y6

= 2x2y2 ! 3x2y + 2x2y2 !1" 2x2y2 ! 4x3y4

Page 4 Your Turn

Factor:6x4y3 + 2x2y2 ! 8x5y6

= 2x2y2 ! 3x2y + 2x2y2 !1" 2x2y2 ! 4x3y4

= 2x2y2 3x2y +1! 4x3y4( )

Page 4 Your Turn

Factor.5x5y + 25x3y3 !15x2y2

Answer:

Here’s how...

5x2y x3 + 5xy2 ! 3x2y( )

Answer:

Here’s how...

5x2y x3 + 5xy2 ! 3x2y( )

5x5y = 5 x x x x x y

25x3y3 = 5 5 x x x y y y

!15x2y2 = !1 5 3 x x y y

5x5y + 25x3y3 !15x2y2

Answer:

Here’s how...

5x2y x3 + 5xy2 ! 3x2y( )

GCF: 5x2y

5x5y = 5 x x x x x y

25x3y3 = 5 5 x x x y y y

!15x2y2 = !1 5 3 x x y y

5x5y + 25x3y3 !15x2y2

Answer:

Here’s how...

5x2y x3 + 5xy2 ! 3x2y( )

GCF: 5x2y

5x5y = 5 x x x x x y

25x3y3 = 5 5 x x x y y y

!15x2y2 = !1 5 3 x x y y

5x5y + 25x3y3 !15x2y2

Answer:

Here’s how...

5x2y x3 + 5xy2 ! 3x2y( )

GCF: 5x2y

5x5y = 5 x x x x x y

25x3y3 = 5 5 x x x y y y

!15x2y2 = !1 5 3 x x y y

5x5y + 25x3y3 !15x2y2

Answer:

Here’s how...

5x2y x3 + 5xy2 ! 3x2y( )

GCF: 5x2y

5x5y = 5 x x x x x y

25x3y3 = 5 5 x x x y y y

!15x2y2 = !1 5 3 x x y y

5x5y + 25x3y3 !15x2y2

Factor:12d 8e3 !18d 5e5 ! 27e8

Answer:

Here’s how...

3e3 4d 8 ! 6d 5e2 ! 9e5( )

Answer:

Here’s how...

3e3 4d 8 ! 6d 5e2 ! 9e5( )

12d 8e3 = 2 2 3 d 5 d 3 e3

!18d 5e5 = !1 2 3 3 d 5 e3 e2

!27e8 = !1 3 3 3 e3 e5

12d 8e3 !18d 5e5 ! 27e8

Answer:

Here’s how...

3e3 4d 8 ! 6d 5e2 ! 9e5( )

GCF: 3e3

12d 8e3 = 2 2 3 d 5 d 3 e3

!18d 5e5 = !1 2 3 3 d 5 e3 e2

!27e8 = !1 3 3 3 e3 e5

12d 8e3 !18d 5e5 ! 27e8

Answer:

Here’s how...

3e3 4d 8 ! 6d 5e2 ! 9e5( )

GCF: 3e3

12d 8e3 = 2 2 3 d 5 d 3 e3

!18d 5e5 = !1 2 3 3 d 5 e3 e2

!27e8 = !1 3 3 3 e3 e5

12d 8e3 !18d 5e5 ! 27e8

Answer:

Here’s how...

3e3 4d 8 ! 6d 5e2 ! 9e5( )

GCF: 3e3

12d 8e3 = 2 2 3 d 5 d 3 e3

!18d 5e5 = !1 2 3 3 d 5 e3 e2

!27e8 = !1 3 3 3 e3 e5

12d 8e3 !18d 5e5 ! 27e8

Answer:

Here’s how...

3e3 4d 8 ! 6d 5e2 ! 9e5( )

GCF: 3e3

12d 8e3 = 2 2 3 d 5 d 3 e3

!18d 5e5 = !1 2 3 3 d 5 e3 e2

!27e8 = !1 3 3 3 e3 e5

12d 8e3 !18d 5e5 ! 27e8

Factor:14a12 ! 28a8 +14a5

Answer:

Here’s how...

14a5 a7 ! 2a3 +1( )

Answer:

Here’s how...

14a5 a7 ! 2a3 +1( )

14a12 = 2 7 a5 a7

!28a8 = !1 2 2 7 a5 a3

21a5 = 2 7 a5

14a12 ! 28a8 + 21a5

Answer:

Here’s how...

14a5 a7 ! 2a3 +1( )

GCF: 14a5

14a12 = 2 7 a5 a7

!28a8 = !1 2 2 7 a5 a3

21a5 = 2 7 a5

14a12 ! 28a8 + 21a5

Answer:

Here’s how...

14a5 a7 ! 2a3 +1( )

GCF: 14a5

14a12 = 2 7 a5 a7

!28a8 = !1 2 2 7 a5 a3

21a5 = 2 7 a5

14a12 ! 28a8 + 21a5

Answer:

Here’s how...

14a5 a7 ! 2a3 +1( )

GCF: 14a5

14a12 = 2 7 a5 a7

!28a8 = !1 2 2 7 a5 a3

21a5 = 2 7 a5

14a12 ! 28a8 + 21a5

Answer:

Here’s how...

14a5 a7 ! 2a3 +1( )

GCF: 14a5

14a12 = 2 7 a5 a7

!28a8 = !1 2 2 7 a5 a3

21a5 = 2 7 a5 No factors but there is an imaginary 1

14a12 ! 28a8 + 21a5

Great Job!You’ve finished reviewing Factoring with a GCF notes.

Exit and proceed to the Mastery Assignment.