how do you factor 4x^4-5x^2-9

Question

its by using Quadratic form

Answer 1

4x^4 - 5x^2 - 9

Let u = x^2. Thus, u^2 = x^4. We have:

4u^2 - 5u - 9
= 4u^2 + 4u - 9u - 9
= (4u^2 + 4u) - (9u + 9)
= (4u)(u + 1) - 9(u + 1)
= (4u - 9)(u + 1)
= (4x^2 - 9)(x^2 + 1)
= ((2x)^2 - 3^2)(x^2 + 1)
= (2x + 3)(2x - 3)(x^2 + 1)

Note that you need to use the formula a^2 - b^2 = (a + b)(a - b)