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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.
|
k·(Ax 2 ± Bx
± C) |
| Given a general trinomial: |
72x 2 − 60x − 28 |
| Factor out common factor if there is one.
|
4(18x 2 − 15x − 7) |
| On Scratch Paper, look at polynomial inside (...): |
18x 2 − 15x − 7 |
| Use GN and Clue of Signs
Multiply first and last coefficients: |
GN
18·7 = 126 |
| NOTE: Last sign is “−” therefore
Find all pairs of factors of 126 with
difference of 15.
|
 |
| The largest factor of the pair gets sign of
middle term, “ − ”
the other is positive:
|
− 21 and + 6 |
| Rearrange polynomial using these values
as coefficients of x |
18x2 − 21x + 6x − 7 |
| Factor common factor from each group: |
3x(6x − 7) + 1(6x −7) |
| Combine with first term factored out
the complete factors of: 72x2 - 60x - 28 |
4(3x + 1)(6x − 7) answer |
| Check by multiplying out: |
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