Factoring Trinomials Worksheet
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Factoring Trinomials where a = 1
1st list all the pairs of factors of c (end term).
Example. x2 + 7x + 12
12
1 12
2 6
3 4
2nd from the list determine which pair of factors will add to the middle term. If no pair
adds to the middle term, then the trinomial is prime.
3rd draw two sets of parenthesis, ( )( ). The factors of the first term, x and x, will
go in the beginning of each parenthesis. The chosen factors from step two will go at
the end of each term. The sign of the factor is the sign between each term.
(x + 3)(x + 4)
Try these, factor.
1. x2 + 6x + 5
2. a2 – 4a + 3
3. b2 – 10b + 16
4. x2 – 14x + 45
5. x2 - 6x - 18
6. x2 - 10x - 24
7. x2 + 5x - 36
8. r2 – 18rt – 144t2
9. p2 + pq – 42q2
Factoring Trinomials where a > 1. Called Fake Factoring.
Example. factor: 2x2 + 5x + 3
2x3=6
2 3
1 6
(2x + 2)(2x + 3)
2
(x + 1)(2x + 3)
1st multiply first and last terms together (a x c). list all the pairs of factors of ac.
2nd from the list determine which pair of factors will add to the middle term. If no pair
adds to the middle term, then the trinomial is prime.
3rd draw two sets of parenthesis, ( )( ). The coefficients of the first term, 2x, will
go in the beginning of each parenthesis. The chosen factors from step two will go at
the end of each term. The sign of the factor is the sign between each term.
4th if either or both parenthesis can be “reduced”, do so.
Try these, factor.
10. 2a2 + 7a + 3
11. 5y2 – 16y + 3
12. 2t2 – t – 6
13. 9n2 + 3n – 2