Final answer:
To factor the trinomial 27n⁴ - 126n² + 147 using the method of factoring by grouping, we can start by factoring out the greatest common factor, which is 3. Then, we can further factor the resulting trinomial as the square of a binomial. The factored form of the given expression is 3(3n² - 7)².
Step-by-step explanation:
To factor the trinomial, we can use the method of factoring by grouping. The given expression is 27n⁴ - 126n² + 147. Notice that all the coefficients are divisible by 3. We can factor out the greatest common factor, which is 3, from all the terms: 3(9n⁴ - 42n² + 49).
Now we have a trinomial that can be factored further.
The trinomial 9n⁴ - 42n² + 49 can be factored as the square of a binomial.
The perfect square trinomial is (3n² - 7)². Therefore, the factored form of the given expression is 3(3n² - 7)².
Learn more about Factoring Trinomials