Questions: Completely factor the trinomial, if possible. 6 b^2 + 11 b + 3

Solution Steps

We start with the trinomial \( 6b^{2} + 11b + 3 \).

To factor the trinomial, we look for two binomials that multiply to give the original trinomial. The factorization is found to be: \[ (2b + 3)(3b + 1) \]

To ensure the factorization is correct, we can expand the factors: \[ (2b + 3)(3b + 1) = 2b \cdot 3b + 2b \cdot 1 + 3 \cdot 3b + 3 \cdot 1 = 6b^{2} + 2b + 9b + 3 = 6b^{2} + 11b + 3 \] This confirms that the factorization is accurate.

Final Answer