To find the required trinomial, start with the product of two binomials and expand it.
Example Trinomial: x^2 - 14x - 15. Factored trinomial: (x-15)(x+1).
Practice makes perfect
Let's consider the following trinomial.
x^2 - 14x - 15
We are interested in factoring the trinomial using the following pattern.
x^2 - 14x - 15 = (x+ p)(x+ m)
In our trinomial, b=-14 and c=-15. Since c is negative, the factors m and p have opposite signs. The fact that b is also negative implies that the factor with the greatest absolute value is negative. Let's look for the pair of factors with a sum of -14.
Factors of -15
Sum of Factors
-15, 1
-14
-5, 3
-2
Next, we substitute p = -15 and m = 1.
x^2 - 14x - 15 &= (x+ p)(x+ m)
&= (x- 15)(x+ 1)
Keep in mind that the trinomial we used is just a sample, and your answer may vary.
Extra
How to Find the Trinomial
To find the required trinomial we can do the process backward. That is, we start with the product of two binomials.
(x- 15)(x+ 1)
Then, using the Distributive Property we expand the product above and combine like terms.
(x- 15)(x+ 1) &= x^2+x-15x-15
&= x^2 - 14x - 15
