How do you factor this polynomial? 16x^4-81?

(4x² - 9)(4x² + 9)
(2x - 3)(2x + 3)(4x² + 9)

Like this: (4x^2+9)(4x^2-9). Or, if your teacher wants it further factored: (4x^2+9)(2x+3)(2x-3)

16x^4-81
(4x^2-9)(4x^2+9)
(2x-3)(2x+3)(4x^2+9)

(4x^2+9)(2x+3)(2x-3)

16x^4 - 81
= (4x^2 + 9)(4x^2 - 9)
= (4x^2 + 9)(2x + 3)(2x - 3)

(x+3)(x-3)(x^2+9), or if using complex numbers,
(x+3)(x-3)(x+3i)(x-3i), where i^2=-1

(4x^2+9)(4x^2-9)
(4x^2+9)(2x^-3)(2x+3)

16x4-81


The binomial can be factored using the difference of perfect roots formula:

(2x-3)(8x3+12x2+18x+27)


Factor the greatest common factor (GCF) from each group.

(2x-3)(4x2(2x+3)+9(2x+3))


Factor the polynomial by grouping the first two terms together and finding the greatest common factor (GCF). Next, group the second two terms together and find the GCF. Since both groups contain the factor (2x+3), they can be combined.

(2x-3)(4x2+9)(2x+3)

Answer:
> (4x^2 + 9) (4x^2 - 9)
> (2x^2 + 3) (2x^2- 3) (4x^2 + 9)