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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Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=+18$
2. $\quad$sum = $-7 \quad$... factors: $-9$ and $+2$
3. $\quad 6x^{2}-7x+3 =(6x^{2}-9x)+( 2x+3)$
4. $\quad$... $=3x(2x-3) +(1)(2x+3) = $... no common factors.
Trying to find another pair of factors of 18 whose sum is $-7$...
... there are none.
The trinomial can't be factored. It is prime.
