Answer
Prime.
Work Step by Step
Factoring by grouping:
1. Multiply the leading coefficient, a, and the constant, c.
2. Find the factors of ac whose sum is b.
3. Rewrite the middle term, bx, as a sum or difference using the factors from step 2.
4. Factor by grouping
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$3x^{2}-5x+1 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=+3\qquad $
2. $\quad$sum = $-5 \quad$... factors: NONE (such pairs exist)
The trinomial can't be factored. It is prime.
