Final answer:
To factor the polynomial 3x²-75, first factor out the common factor of 3 to get 3(x² - 25), then use the difference of squares formula to factor further into 3(x + 5)(x - 5).
Step-by-step explanation:
To factor the polynomial 3x²-75, we can look for common factors in both terms. Here, both terms have a common factor of 3. Additionally, we recognize that 75 is a multiple of 3. Factoring out the 3, we get:
3(x² - 25).
Next, we see that x² - 25 is a difference of squares since 25 is a perfect square (5²). Remember that the difference of squares formula is a² - b² = (a + b)(a - b). Applying this to the expression inside the parentheses, we get:
3(x + 5)(x - 5).
So, the fully factored form of 3x²-75 is 3(x + 5)(x - 5).