General Trinomial Factoring

Steps:

1) Multiply the leading coefficient and the constant together.

2) List all possible factors from the result in step 1.

3) Determine which factors will add together to give the middle coefficient.

4) Write the middle coefficient as the sum of the factors using the results from step 3 and rewrite the polynomial.

5) Group the first two terms and the last two terms together.

6) Factor the greatest common factor from each group.

7) Factor the greatest common factor again.

8) Check your answer using the FOIL method and compare it to the original trinomial.



Example 1:
2x^2 + 17x + 26 Multiply 2 x 26 = 52
Factors of 52 are 1 and 52, 2 and 26, 4 and 13, -1 and -52, -2 and -26, -4 and -13
Sum of the factors that equal the middle term are 4 + 13
Rewrite the middle term as the sum of the factors which is 2x^2 + 4x + 13x + 26
Group terms (2x^2 + 4x) + (13x + 26)
Factor Greatest Common Factor (GCF) 2x(x + 2) + 13(x + 2)
Factor GCF again (x + 2)(2x + 13)


Try These to Practice:
1) x^2 + 5x + 4

2) 3x^2 + 17x + 10

3) 3k^2 + 32k - 11

4) 5x^2 + 3x - 2





ANSWERS







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Factoring Perfect Square Trinomials