To factor the expression x³ + 3x², we first look for common factors in both terms. Both terms have x² as a common factor.
We can factor x² out of the expression:
x²(x + 3)
Thus, the complete factorization of the expression x³ + 3x² is:
x²(x + 3)
This factorization tells us that if we set the expression equal to zero, we can find the roots:
- x² = 0 gives the root x = 0 (with multiplicity 2),
- x + 3 = 0 gives the root x = -3.
In conclusion, the complete factorization not only simplifies the expression but also helps in understanding the zeros of the polynomial.