factor completely 3x^4+6x^3-45x^2

Question

I need to know the steps to factor completely.

Thank you.

Answer 1

The polynomial is 3x ^4 + 6x ^3 - 45x ^2.

Factor by grouping.

3x ^4 + 15x ^3 - 9x ^3 - 45x ^2

3x ^3(x + 5) - 9x ^2(x + 5)

Factor : (x + 5)(3x ^3 - 9x ^2)

Factor by grouping.

(x + 5)3x ^3 - 9x ^2 = (x + 5)3x ^2(x - 3)

Therefore, the complete factor of 3x ^4 + 6x ^3 - 45x ^2 = 3x ^2(x + 5)(x - 3).