Factor 3v^2-42y+144

To factor the expression 3v^2-42y+144, we can look for common factors and use the basic factoring techniques.

First, let's see if there is a common factor among the coefficients (3, -42, and 144). The greatest common factor (GCF) is 3.

Next, let's look at the variables. The given expression has terms with v and y. However, there is no common variable factor between them.

Now, let's factor out the GCF of 3 from each term:
3v^2-42y+144 = 3(v^2 - 14y + 48)

To further factor the expression inside the parentheses, we need to find two numbers whose product is 48 (the constant term - coefficient of v^2) and sum is -14 (the coefficient of y). Those numbers are -6 and -8.

Therefore, the fully factored form of 3v^2-42y+144 is 3(v - 6)(v - 8).