Answer:
2x(x - 2)(x - 5)
Explanation:
To factor the trinomial 2x³ - 14x² + 20x completely, let's first look for the greatest common factor (GCF) among the terms.
The GCF of the terms 2x³, -14x², and 20x is 2x. By factoring out the GCF, we get:
=> 2x(x² - 7x + 10)
Now, let's factor the quadratic trinomial inside the parentheses: x² - 7x + 10. This can be factored as follows:
=> x² - 7x + 10 = (x - 5)(x - 2)
Therefore, the completely factored form of the trinomial 2x³ - 14x² + 20x is:
=> 2x(x - 5)(x - 2)