To factorize the expression 6x\(^2\) + 7xy - 5y\(^2\), we need to find two binomials whose product equals the expression.
First, we need to find two numbers that multiply to 6, the coefficient of the x\(^2\) term, and two numbers that multiply to -5, the coefficient of the y\(^2\) term. We also need to find the signs of the two numbers that add up to 7, the coefficient of the xy term.
After some trial and error, we can determine that the factors are (3x - y) and (2x + 5y). Multiplying these two binomials using FOIL method, we get:
(3x - y)(2x + 5y) = 6x\(^2\) + 7xy - 5y\(^2\)
Therefore, the correct answer is option (D): (3x + 5y)(2x - y).