Final answer:
To factor the polynomial 2y² + 15y + 7, we rewrite the middle term as 14y + y and then group and factor out common factors to get the final factored form (2y + 1)(y + 7).
Step-by-step explanation:
To factor the polynomial 2y² + 15y + 7 using the grid method, we look for two numbers that multiply to (2 · 7) = 14 and add up to 15. These numbers are 14 and 1. Once we find these numbers, we can rewrite the middle term, 15y, as 14y + y.
The polynomial then becomes 2y² + 14y + y + 7. Grouping terms together gives us (2y² + 14y) + (y + 7). Factoring out the common factors from each group gives us 2y(y + 7) + 1(y + 7). Finally, since (y + 7) is a common factor, we can factor it out to get the final factored form of (2y + 1)(y + 7).
Thus, the polynomial factors to (2y + 1)(y + 7).