Questions: Factor completely by using the trial-and-error method. Select "Prime" if the polynomial cannot be factored. 2 w^2+11 w+5= Prime

Solution Steps

To factor the quadratic polynomial \(2w^2 + 11w + 5\) using the trial-and-error method, we need to find two binomials whose product gives the original polynomial. We look for pairs of factors of the constant term (5) and the leading coefficient (2) that combine to give the middle term (11w).

We start with the quadratic polynomial given by \[ 2w^2 + 11w + 5. \]

Using the trial-and-error method, we find the factors of the polynomial. The polynomial can be factored as follows: \[ 2w^2 + 11w + 5 = (w + 5)(2w + 1). \]

To ensure the factorization is correct, we can expand the factors: \[ (w + 5)(2w + 1) = w \cdot 2w + w \cdot 1 + 5 \cdot 2w + 5 \cdot 1 = 2w^2 + w + 10w + 5 = 2w^2 + 11w + 5. \] This confirms that the factorization is accurate.

Final Answer