#"using the a-c method of factoring the quadratic in "x^4#

#"the factors of the product "3xx-1=-3#

#"which sum to - 2 are - 3 and + 1"#

#"split the middle term using these factors"#

#3x^4-3x^2+x^2-1larrcolor(blue)"factor by grouping"#

#=color(red)(3x^2)(x^2-1)color(red)(+1)(x^2-1)#

#"take out the "color(blue)"common factor "(x^2-1)#

#=(x^2-1)(color(red)(3x^2+1))#

#x^2-1" is a "color(blue)"difference of squares"#

#"and factors in general as"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#rArrx^2-1=(x-1)(x+1)#

#rArr3x^4-2x^2-1=(3x^2+1)(x-1)(x+1)#