2y^2 + 5y – 42

Answer 1

To factor the trinomial 2y^2 + 5y - 42, we need to find two numbers that multiply to 2*(-42) = -84 and add up to 5.

The two numbers are 12 and -7, because 12*(-7) = -84 and 12 + (-7) = 5.

Now we can rewrite the middle term using these two numbers:
2y^2 + 12y - 7y - 42

Factor by grouping:
2y(y + 6) - 7(y + 6)

Factor out the common factor of (y + 6):
(y + 6)(2y - 7)

Therefore, the factored form of 2y^2 + 5y - 42 is (y + 6)(2y - 7).