Example solutions for factoring a two termed quadratic expression by taking the common factor

• Example 1:    9x² + 3x
  

  3(3x2 + x)	. . . Taking 3 as a common factor.
  3x(3x + 1)	. . . Taking 'x' as the common factor.

  Answer: 3x(3x + 1)

• Example 2:    2x² - 3x
  

  x(2x - 3)

  . . . Taking 'x' as the common factor.

  Answer: x(2x - 3)

• Example 3:    8x² + 15
  

  Answer: The given expression is a prime expression. It cannot be factored since no number or variable is common to both terms

• Example 4:    3ax² + 8abx

  x(3a + 8ba)	. . . 'x' is the common factor
  xa(3 + 8b)	. . . 'a' is the common factor

  Answer: xa(3 + 8b)

• Example 5:    4x² - 3x

  x(4x - 3)

  . . . 'x' is the common factor

  Answer: x(4x - 3)

• Example 6:    √3x² + 3

  √3(x + √3)

  . . . '√3' is the common factor

  Answer: √3(x + √3)

• Example 7:    ax² + bx

  x(ax + b)

  . . . 'x' is the common factor

  Answer: x(ax + b)

• Example 8:    35x² - 2

  Answer: The given expression is a prime expression. It has no common factor

  
  

• Example 9:    (a + b)x² + a + b

  (a + b)(x2 + 1)

  . . . '(a + b)' is the common factor

  Answer: (a + b)(x2 + 1)

  
  

• Example 10:

  	. . . 'x' is the common factor
  	. . . '1/2' is the common factor

  Answer: