Question

Factor completely 3pa-180a^2+p^2.

Answer 1

your answer is ; (p-12a)(p+15a)

Answer 2

You would need to find factors of -180 that sum to 3. Those would be 15 and -12, so the factorization is

... (p -12a)(p +15a)

_____

If we assume the factors are

... (p + m·a)(p +n·a)

then their product is

... p² + (m+n)·pa + m·n·a²

Comparing this to the given trinomial, we see m and n are factors of -180, and their sum is 3.