5x4 − 80. Rewritten as 5X^4 - 80 = 5(X^4 - 16)
5(X^2 + 4)(X^2 - 4)
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)
3 answers
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 )
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 )
oops. I didn't finish factoring the X^2 - 4.