How do you factor f(x)= x^4 - 9x^2?

1 Answer
May 15, 2018

=x^2*(x-3)(x+3)

Explanation:

x^4 - 9x^2

take x^2 as a common factor:

color(red)(x^2)*(x^2-9)

now what is inside the parentheses we can factor them by the difference between two squares formula: color(blue)(x^2-9=x^2-3^2)

now difference between two squares formula


a^2 - b^2 = (a-b)(a+b)


color(blue)(x^2-3^2 = (x-3)(x+3))


=color(red)(x^2)*color(blue)((x-3)(x+3))

=x^2*(x-3)(x+3)