4.4 Factoring Quadratic Expressions
Vocabulary:
 Factoring: Rewriting an expression as the product of its factors.
 G.C.F of an Expression: A common factor of the terms of the expression. You
can factor any expression that has a G.C.F. not equal to 1.
 Quadratic Trinomial: An expression in the form y = ax² + bx + c, that can be
factored into two binomial factors.
1. Find two factors of the “a” quadratic term & the “c” constant term.
2. Multiply the Inner Terms & the Outer Terms, then find the sum “b.”
Rules:
ax2 + bx + c: (+)(+)
ax2 - bx + c: (-)(-)
ax2 + bx - c: (+)(-)
ax2 - bx – c: (-)(+)
I. Factoring
Example 1: Finding Common Factors
Factor each expression.
1a) 4x² + 20x – 12
GCF:
1c) 9x² + 3x – 18
1b) 9n² - 24n
GCF:
1d) 7p² + 21
Example 2: Factoring ac > 0 and b > 0
 If ac and b are positive, then factors of ac are both positive.
 When ax² + bx + c; Binomial set up: ( + ) ( + ).
 Multiply the Inner Terms & the Outer Terms, then find the sum “b”. This helps
you check your binomial set up.
2a) x² + 8x + 7
2b) x² + 14x + 40
Example 3: Factoring When ac > 0 and b < 0.
 If ac is positive and b is negative, then the factors of ac are both negative.
 When ax² - bx + c; Binomial set up: ( - ) ( - ).
 Multiply the Inner Terms & the Outer Terms, then find the sum “b”. This helps
you check your binomial set up.
3a) x² - 17x + 72
3b) x² - 11x + 24
Example 4: Factoring When ac < 0
 If ac is negative, then the factors of ac have different signs.
 When ax² - bx - c; Binomial set up: ( - ) ( + ) or ( + ) ( - ).
 Multiply the Inner Terms & the Outer Terms, then find the sum “b”. This helps
you check your binomial set up.
4a) x² - x - 12
4b) x² + 3x – 10
Example 5: Factoring When a ≠ 1 and ac > 0
 The rules for the setup when ac are positive like in examples 2 & 3, then the
factors of ac have the same sign. This is true even when a ≠ 1.
 When ax² + bx + c; Binomial set up: ( + ) ( + )
 When ax² - bx + c; Binomial set up: ( - ) ( - ).
 Multiply the Inner Terms & the Outer Terms, then find the sum “b”. This helps
you check your binomial set up
5a) 3x² - 16x + 5
5b) 4x² - 7x + 3
5c) 2x² + 11x + 12
Example 6: Factoring When a ≠ 1 and ac< 0
 If ac is negative, then the factors of ac have different signs.
 When ax² - bx - c; Binomial set up: ( - ) ( + ) or ( + ) ( - ).
 Multiply the Inner Terms & the Outer Terms, then find the sum “b”. This helps
you check your binomial set up
6a) 4x² - 4x - 15
6b) 3x² - 16x – 12
6c) 4x² + 5x – 6
II. Factoring Special Expressions
Vocabulary:
 Perfect Square Trinomial: Is the product you obtain when you square a binomial.
a² + 2ab + b² = (a + b)²
or a² - 2ab + b² = (a - b)²
1a) x2 + 10x + 25
1b) x2 -14x + 49
Example 2a) 9x² - 42x + 49
 Rewrite the first and third terms as simplified squares.
 Then write its has a square binomial (a + b)² or (a - b)²
1b) 64x² - 16x +1
Difference of Two Squares: (a² - b²) = (a + b) (a - b)
2a) x² - 64
2b) 4a² - 49