| WHAT TO DO:
|
HOW TO DO IT: |
| Given a trinomial of type ax2 + bx + c that has
no common factor, where signs may be positive or
negative. Separate the signs from the coefficients.
[Read ± as + or - ]
Read the “clues of the signsâ€.
|
 |
| Find product of first and last coefficients.
This is the grouping number (GN)
|
GN
A·C = P |
| Find all possible factors of GN = P
whose sum or difference is B
(depending on the sign before C.)
+ sum
or
- difference |
P = r·s
, r > s (r + s) = B
(r - s) = B |
| Example:
Given: 10x2 + 11x - 6 |
GN
10·6 = 60 |
| The last sign is “−†so find the pair of factors
of 60 that has a difference of 11.
|
 |
| The largest factor of the pair gets middle sign, +
|
+ 15 and
- 4 |
| The trinomial can be arranged in four terms using
these values as coefficients of x, grouped 2 × 2 |
10x2
+ 15x − 4x − 6 |
| Factor common factor from each group:
|
5x(2x + 3) − 2(2x + 3) |
| Find common term in ( ), factor: |
(5x − 2)(2x + 3) |
| Check by FOIL method.
Always Check· |
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