Final answer:
To factor the polynomial 2x³+3x²−50x−75 completely by grouping, we can group the terms and factor out the common factors. The factored form is (2x+3)(x−5)(x+5).
Step-by-step explanation:
To factor the polynomial 2x³+3x²−50x−75 completely by grouping, we can start by grouping the terms in pairs. Let's group the first two terms and the last two terms:
(2x³+3x²)−(50x+75)
We can factor out the greatest common factor from each pair:
x²(2x+3)−25(2x+3)
Now we can see that we have a common factor of (2x+3) in each term. So we can factor that out:
(2x+3)(x²−25)
Finally, we can simplify the expression by factoring x²−25 as a difference of squares:
(2x+3)(x−5)(x+5)