Factor 3v^2-42v+144

To factor 3v^2 - 42v + 144, we need to find two numbers that multiply to 144 and add up to -42.

The prime factorization of 144 is 2 * 2 * 2 * 2 * 3 * 3, or 2^4 * 3^2.

The pairs of numbers that multiply to 144 are:
1, 144
2, 72
3, 48
4, 36
6, 24
8, 18
9, 16
12, 12 (the two numbers are the same)

Out of these pairs, the numbers that add up to -42 are 6 and 24.

So, we can rewrite -42v as 6v - 24v.

Therefore, 3v^2 - 42v + 144 factors as 3v^2 + 6v - 24v + 144.

Now, we can group the terms:

(3v^2 + 6v) - (24v - 144)

Next, we factor out the greatest common factor from each group:

3v(v + 2) - 24(v - 6)

Finally, we combine the terms:

3v(v + 2) - 24(v - 6) = (v + 2)(3v - 24)

So, the factored form of 3v^2 - 42v + 144 is (v + 2)(3v - 24).