1.  1x3 - 26x2 + 48x

Take out x

x(1x2 - 26x + 48)

Multiply the +48 times the 1 before the x2, getting +48
I. Think of two numbers which
A) multiply to give +48
and which also
B) combine to give -26

It doesn't take long to think of -2 and -24 because
A) -2 TIMES -24 gives +48
and
B) -2 PLUS -24 gives -26

II. Write -26x using -2 and -24
   -26x = -2x - 24x

III. Replace -26x in
   x(x2 - 26x + 48)
   
   with -2x - 24x
   
   x(x2 - 2x - 24x + 48)

IV. Change the parentheses to brackets:
   x[x2 - 2x - 24x + 48]

V. Factor out x in the first two terms in the brackets  

   x[x(x - 2) - 24x + 48]

VI. Factor out -24 in the last two terms in the brackets  

   x[x(x - 2) - 24(x - 2)]

VII. Factor out the common factor (x - 2) within the brackets

   x[(x - 2)(x - 24)]

VIII. Erase the brackets:

   x(x - 2)(x - 24)

------------------------------------ 

2.   x2 - 6wy + 3xy - 2wx

I. We can't factor the first two terms, so we must rearrange terms

   x2 + 3xy - 2wx - 6wy

II. Factor x out of the first two terms   

   x(x + 3y) - 2wx - 6wy 

III. Factor -2w out of the last two terms

   x(x + 3y) - 2w(x + 3y) 
  
IV. Factor out common factor (x + 3y)

   (x + 3y)(x - 2w)

-----------------------------

3.   1x2 - 5x - 14

Multiply the -14 times the 1 before the x2, getting -14
I. Think of two numbers which
A) multiply to give -14
and which also
B) combine to give -5

It doesn't take long to think of -7 and +2 because
A) -7 TIMES +2 gives -14
and
B) -7 PLUS +2 gives -5

II. Write -5x using -7 and +2
   -5x = -7x + 2x

III. Replace -5x in

   x2 - 5x - 14

   with -7x + 2x
   
   x2 - 7x + 2x - 14

IV. Factor x out of the first two terms:

  x(x - 7) + 2x - 14

V. Factor +2 out of the last two terms:

  x(x - 7) + 2(x - 7) 

VI. Factor out common factor (x - 7)  

  (x - 7)(x + 2)

------------------------

4.   4x2 - 36y2

First factor out 4

  4(x2 - 9y2)

Change parentheses to brackets and write each as a perfect square

  4[(x)2 - (3y)2]

This is the difference of two perfect squares
Learn formula: A2 - B2 factors as (A - B)(A + B)

  4[(x) - (3y)][(x) + (3y)]

Remover the inner parentheses

  4[x - 3y][x + 3y]

Change brackets to parentheses

  4(x - 3y)(x + 3y)  

-------------------------------

5.   3x2 - 2x - 8

Multiply the -8 times the 3 before the x2, getting -24
I. Think of two numbers which
A) multiply to give -24
and which also
B) combine to give -2

It doesn't take long to think of -6 and +4 because
A) -6 TIMES +4 gives -24
and
B) -6 PLUS +4 gives -2

II. Write -2x using -6 and +4
   -2x = -6x + 4x

III. Replace -2x in

   3x2 - 2x - 8

   with -6x + 4x
   
   3x2 - 6x + 4x - 8

IV. Factor 3x out of the first two terms:

  3x(x - 2) + 4x - 8

V. Factor +4 out of the last two terms:

  3x(x - 2) + 4(x - 2) 

VI. Factor out common factor (x - 2)  

  (x - 2)(3x + 4)

----------------------------

6.   24x2 + 10x - 4

Take out 2

2(12x2 + 5x - 2)

Multiply the -2 times the 12 before the x2, getting -24
I. Think of two numbers which
A) multiply to give -24
and which also
B) combine to give +5

It doesn't take long to think of +8 and -3 because
A) +8 TIMES -3 gives -24
and
B) +8 PLUS -3 gives +5

II. Write +5x using +8 and -3
   +5x = +8x - 3x

III. Replace +5x in

2(12x2 + 5x - 2)
      
   with +8x - 3x
   
   2(12x2 + 8x - 3x - 2)

IV. Change the parentheses to brackets:

   2(12x2 + 8x - 3x - 2)

V. Factor out 4x in the first two terms in the brackets  

   2[4x(3x + 2) - 3x - 2]

VI. Factor out -1 in the last two terms in the brackets  

   2[4x(3x + 2) - 1(3x + 2)]

VII. Factor out the common factor (3x + 2) within the brackets

   2[(3x + 2)(4x - 1)]

VIII. Erase the brackets:

   2(3x + 2)(4x - 1)

Edwin
AnlytcPhil@aol.com