Question

Explain, in complete sentences, how you would factor 27x4 – 90x2 + 75.

Provide the factors.

Answer 1

First factor 3 out. You get 3(9x^4 - 30x^2 + 26).
Then, find the roots of that quadratic (well, it is a quadratic if you substitute x^2 = y or something). See if there are real roots, and hopefully integer roots. Then, you can factor further.

Answer 2

That is 25 not 26. Sorry.

Answer 3

It turns out 9x^4 - 30x^2 + 25 is a perfect square. So, it factors to: (3x-5)^2.
So, the factors are: 3(3x-5)^2