| WHAT TO DO: |
HOW TO DO IT: |
| Given general trinomial of type that has
no common factor. Read the "clues of the
signs". [Read ± as + or - ]
|
 |
| The constant c is the grouping
number |
GN = c |
| Find all possible factors of GN = c whose
sum or difference is b
(depending on the sign before c .)
+ sum or
- difference
|
c = r · s , r > s (r + s) = b
(r - s) = b
|
| 1. Consider the trinomial : x 2
- 5x + 6 The leading coefficient is 1 and the last
sign is +
The factors of 6 with a sum of 5 are 3 and 2
Since the last sign is + the "same sign" in
both binomials is - (the sign of the middle term).
Factor by grouping. Bring down the middle sign.
Complete the factors.
|
1. x 2 - 5x + 6 r · s = 6
and r + s = 5
|
| 2. First, examine the trinomial to see
if it has a common factor(s) in each term. Check the
remaining trinomial to see if it will factor: |
2. 3x 2 +15x + 12 3(x
2 + 5x + 4)
|
| 2a) Consider the trinomial :
x 2 + 5x + 4 The leading coefficient is 1
and the last sign is + The factors of 4 with a sum of 5
are 4 and 1 Since the last sign is + the "same
sign" in both binomials is + (the sign of the middle
term).
Factor by grouping. Bring down the middle sign.
Complete the factors.
|
2a) x 2 + 5x + 4 r
· s = 4 and r + s = 5
|
| 2b) Go back to the
polynomial in the previous step: Replace the polynomial
with the factors to find all of the factors: 3x 2
+15x + 12 |
2b) 3(x 2 + 5x +
4) = 3(x + 1)(x + 4)
|
| 3. Consider the trinomial
with last sign + Two numbers with a product of 14 and
sum of are 7 and 2
Rewriting the terms to factor by grouping:
|
3. x 2 + 9x + 14 x
2 + 7x + 2x + 14
|
| Then group the terms 2 × 2
into two terms. Factor common factors. Bring down the
middle sign.
Find the common factor for each group.
|
 |
| Factor out the common factor |
(x + 7)(x + 2) Answer |
| Check by multiplying back out by |
F 0 I L |
| FOIL method. First - Outer - Inner -
Last
Note O-I terms.
|
 |
