Question

Factor completely 5x4 − 80.

5(x2 − 4)(x2 + 4)
5(x − 2)(x + 2)(x + 2)(x + 2)
5(x − 2)(x + 2)(x2 − 4)
5(x − 2)(x + 2)(x2 + 4)

Answer 1

5x4 − 80. Rewritten as 5X^4 - 80 = 5(X^4 - 16)
5(X^2 + 4)(X^2 - 4)

Answer 2

5 x⁴ - 80 = 5 ( x⁴ - 16 )

To factor x⁴ - 16 can use difference of squares formula:

a² - b² = ( a - b ) ( a +b )

In this case:

a = x²

because

x⁴ = ( x² )²

b = 4

because

16 = 4²

so

x⁴ - 16 = ( x² )² - 4² = ( x² - 4 ) ( x² + 4 )

To factor x² - 4 again can use difference of squares formula:

a² - b² = ( a - b ) ( a + b )

In this case:

a = x

b = 2

x² - 4 = ( x )² - ( 2 )² = ( x - 2 ) ( x + 2 )

x⁴ - 16 = ( x² - 4 ) ( x² + 4 ) = ( x - 2 ) ( x + 2 ) ( x² + 4 )

5 x⁴ - 80 = 5 ( x⁴ - 16 )

5 x⁴ - 80 = 5 ( x - 2 ) ( x + 2 ) ( x² + 4 )

Answer 3

oops. I didn't finish factoring the X^2 - 4.