Answer:
3x(x+5)(x-2)
Explanation:
You want the complete factorization of 3x^3 + 9x^2 - 30x after first removing the greatest common factor.
GCF
The greatest common factor will be the lowest powers of the factors that are common to the three terms:
3·x³
3²·x²
2·3·5·x
The common factors are 3 and x. Their lowest powers are 1, so the GCF is 3x.
Finish factoring
After factoring out 3x, we have a quadratic factor:
= 3x(x² +3x -10)
To factor this, we look for factors of -10 that have a sum of +3. Those are -2 and +5. This tells us the complete factorization is ...
= 3x(x -2)(x +5)