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Showing Is a Prime Trinomial
Attempt to factor by applying the ac method for trinomials with a leading coefficient other than 1.
Step 1 — Check for a GCF. The terms , , and share no common factor, so proceed.
Step 2 — Find the product . Here and , so .
Step 3 — Find two numbers that multiply to 10 and add to 6. List all factor pairs of 10 and check their sums:
| Factors of | Sum of factors |
|---|---|
Neither factor pair produces a sum of 6.
Since no pair of integers has a product of 10 and a sum of 6, the trinomial cannot be factored — it is a prime polynomial. This example extends the concept of prime trinomials to expressions of the form where : instead of looking for factor pairs of the constant term , the ac method requires factor pairs of the product . When no such pair has the correct sum, the trinomial is prime regardless of whether the leading coefficient is 1 or not.
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Showing Is a Prime Trinomial
Showing Is a Prime Trinomial
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