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

1 Answer
May 15, 2018

Answer:

#=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)#