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WHAT TO DO:
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HOW TO DO IT: |
| Given a trinomial of type
ax2 + bx + c that has at
least one common factor. Factor out all of the common
factors then look at the remaining quadratic trinomial. |
ax 2 + bx + c
k·(Ax 2 ± Bx ± C) |
| Given a general trinomial: |
12x 2 y − 33xy − 9y |
|
Factor out common factor if there is one.
|
3y(4x 2 − 11x − 3) |
| On Scratch Paper, look at the polynomial inside ( ):
|
4x 2 − 11x − 3 |
| Consider Clue of Signs and GN
→ multiply first and last coefficients:
|
GN:
4·3 = 12 |
| Last sign is “−” therefore
Find all pairs of factors of 12 with
difference of 11.
|
 |
| The largest factor of the pair gets sign of
middle term, “ − ”
the other is positive:
|
− 12 and + 1 |
| Rearrange polynomial using these values
as coefficients of x |
4x 2 − 11x + 1x − 9 |
|
Factor common factor from each group: |
4x(x − 3) + 1(x −3) |
|
Combine these with first term factored out, 3y , to get
the complete factors of: 12x 2 y − 33xy − 9y
→ |
(4x + 1)(x − 3)
3y(4x + 1)(x − 3) answer |
| Check by multiplying out: |
 |
