Algebra 2: Section 4.5 Factoring Notes
Name: _________________________
Example 1: Multiply the two binomials. **This is a double distribution!
(2 x  4)(x  1)  ___(x  1)  ___(x  1) =
Example 2: Write an expression for the area of the rectangle.
Example 3: Find the missing terms in the figure below.


Above is an organizer to assist in multiplying binomials.
When we multiplied, we often get a quadratic. The ________________of a quadratic is ax 2  bx  c  0 .
Today, we will see two methods to factor! **essentially we are “undoing” the multiplication
Example 4:
Box Method
Factor by Grouping
2x  7x  5
2x2  7 x  5
2
Step 1: Find the product ( ac )
Step 2: Find the sum (b).
Step 3: Rewrite
(
) +(
)
Step 4: Factor out a GCF (and work backwards to match)
__ (
Step 5: Write in factored form.
) + __(
)
Example 5:
Box Method
Factor by Grouping
3x  8 x  4
3x 2  8 x  4
2
Step 1: Find the product ( ac )
Step 2: Find the sum (b).
Step 3: Rewrite
(
) +(
)
Step 4: Factor out a GCF (and work backwards to match)
__ (
) + __(
)
Step 5: Write in factored form.
Example 6:
Box Method
Factor by Grouping
x  5x  6
x2  5x  6
2
Step 1: Find the product ( ac )
Step 2: Find the sum (b).
Step 3: Rewrite
(
) +(
)
Step 4: Factor out a GCF (and work backwards to match)
__ (
Step 5: Write in factored form.
) + __(
)
Try It!
a) Factor 2 x 2  7 x  3
Box Method
Factor by Grouping
2x  7x  3
2x2  7 x  3
2
Step 1: Find the product ( ac )
Step 2: Find the sum (b).
Step 3: Rewrite
(
) +(
)
Step 4: Factor out a GCF (and work backwards to match)
__ (
Step 5: Write in factored form.
b) Factor 3x 2  5 x  12
Step 1: Find the product ( ac )
Step 2: Find the sum (b).
Step 3: Rewrite
Step 4: Factor out a GCF (and work backwards to match)
Step 5: Write in factored form.
) + __(
)