Final answer:
The question is about factoring a polynomial expression in Mathematics. To factor 5x³ + 15x² - 50x, first factor out the GCF of 5x, resulting in 5x(x² + 3x - 10), then factor the quadratic to obtain the final result of 5x(x + 5)(x - 2).
Step-by-step explanation:
The question asks to define the subject which is clearly related to Mathematics, specifically algebraic expressions or polynomial factoring. The expression given can be simplified: 5x³ + 15x² - 50x. All terms share a common factor of 5x, therefore, we can factor it by using the distributive property:
- Factor out the greatest common factor (GCF), which is 5x.
- Rewrite the expression as 5x(x² + 3x - 10).
- Now factor the quadratic trinomial x² + 3x - 10.
- This can be factored into (x + 5)(x - 2), assuming that the quadratic factors nicely over the integers.
- The fully factored form of the original expression is 5x(x + 5)(x - 2).
Remember, when factoring, you're looking for products that when multiplied together give the original quadratic expression, and whose sum gives the middle term's coefficient.