factor out completely

Question

Factor completely:

Answer 1

-3a⁴ + 24a³ - 36a² = ?

Note the common factor is 3a².

-3a⁴ + 24a³ - 36a² = 3a²(-a² + 8a -12) = -3a²(a² - 8a + 12)

Note that

a² - 8a + 12 = (a - 2)(a - 6)

Then the complete factorization gives

-3a⁴ + 24a³ - 36a² = -3a²(a - 2)(a - 6)