Question

Factor out the greatest common factor. if the greatest common factor is 1, just retype the polynomial.

48n⁴ - 3n²

Answer 1

3n²(4n - 1)(4n + 1)

Explanation:

given

48
`n^(4)` - 3n² ← factor out 3n² ( the greatest common factor )

= 3n²(16n² - 1) ← 16n² - 1 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

16n² - 1

= (4n)² - 1² [ with a = 4n and b = 1 ]

= (4n - 1)(4n + 1)

Then

48
`n^(4)` - 3n²

= 3n²(4n - 1)(4n + 1) ← in factored form