7.3 Factoring Trinomials
Geometry
Section 7.3
Remember!
When you multiply two binomials, multiply:
First terms
Outer terms
Inner terms
Last terms
OR
BOX method
First terms
Outer terms
Inner terms
x2
12
Last terms
(x + 3)(x +4) = x2 + 7x + 12
3x
4x
The first term is the product of x and x. The
coefficient of the middle term is the sum of 3 and
4. The third term is the product of 3 and 4.
Using FOIL or Box method, solve these three
problems.
(x - 5)(x +1) = x2 - 4x - 5
(2x + 1)(x -7) = 2x2 - 13x - 7
(x + 6)(x -6) = x2 - 36
Factoring is reversing the FOIL method. You are
given the full quadratic equation. From this
equation, you must break up the equation into
two sets of parenthesis
Example
x2 + 7x + 10
(x + 2)(x + 5)
1. Set your parenthesis
2. Separate your X’s
3. Find factors for the ‘C’
value
4. Manipulate the factors so
that the values combined
will equal the ‘B’ value
When c is positive, its factors have the same
sign. The sign of b tells you whether the factors
are positive or negative. When b is positive, the
factors are positive and when b is negative, the
factors are negative.
Example 1A: Factoring Trinomials by Guess and
Check
Factor.
x2 + 6x + 5
(x + )(x+ )
Factors of 5 Sum
1 and 5
x2 + 6x + 9
(x + )(x+ )
Factors of 9 Sum
1 and 9
10 
3 and 3
6
6
x2 – 8x + 15
(x - )(x - )
Factors of 15 Sum
1 and 15 16 
3 and 5 8 
Example 1A: Factoring Trinomials by Guess and
Check
Factor.
x2 + 8x + 12
(x +
)(x+
Factors of 12
1 and 12
2 and 6
)
Sum
13
8
x2 – 5x + 6
(x - )(x- )
Factors of 6 Sum
1 and 6 7 
2 and 3 5 
Example 1A: Factoring Trinomials by Guess and
Check
Factor.
x2 + 13x + 42
(x +
)(x +
)
Factors of 42 Sum
1 and 42 43 
2 and 21 23 
6 and 7 13 
x2 – 13x + 40
(x -
)(x-
)
Factors of 40 Sum
2 and 20
22 
4 and 10
14 
5 and 8
13 
When c is negative, its factors have
opposite signs. The sign of b tells you which
factor is positive and which is negative. The
factor with the greater absolute value has the
same sign as b.
Example 1A: Factoring Trinomials by Guess and
Check
Factor.
x2 – 3x – 18
x2 + x – 20
(x -
)(x +
)
Factors of 20 Sum
1 and 20
19 
2 and 10
8
4 and 5
1
(x -
)(x +
)
Factors of 18 Sum
1 and 18
17 
2 and 9
7
3 and 6
3
Helpful Hint
If you have trouble remembering the rules for
which factor is positive and which is negative,
you can try all the factor pairs and check their
sums.
Check It Out! Example 3a
Factor.
x2
x2 – 6x + 8
+ 2x – 15
(x -
)(x +
)
Factors of 15 Sum
1 and 15
14 
3 and 5
2
(x -
)(x -
Factors of 8
1 and 6
2 and 4
)
Sum
7
6
Check It Out! Example 3c
Factor.
X2 – 8x – 20
(x +
)(x -
)
Factors of 20 Sum
1 and 20 19 
2 and 10
8 