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Showing Is a Prime Trinomial
Attempt to factor by applying the trinomial factoring strategy. The constant term 15 is positive and the middle coefficient is negative, so both numbers in the factor pair must be negative.
Step 1 — Set up two binomials with first terms : .
Step 2 — Find two negative numbers that multiply to 15 and add to . List all negative factor pairs of 15 and check their sums:
| Factors of 15 | Sum of factors |
|---|---|
Neither factor pair produces a sum of . Since no pair of integers has a product of 15 and a sum of , the trinomial cannot be factored — it is a prime trinomial.
This example illustrates the method for confirming that a trinomial is prime: systematically list every possible factor pair, show that none of them yield the required sum, and conclude that the expression is already in its simplest form.
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