How do you factor #x ^ { 4} + 2x ^ { 2} + 1# completely?
1 Answer
Apr 10, 2018
Explanation:
#"the factors of + 1 which sum to + 2 are + 1 and + 1"#
#"split the middle term using these factors"#
#x^4+x^2+x^2+1larrcolor(blue)"factor by grouping"#
#=color(red)(x^2)(x^2+1)color(red)(+1)(x^2+1)#
#"take out the common factor "(x^2+1)#
#=(x^2+1)(color(red)(x^2+1))#
#rArrx^4+2x^2+1=(x^2+1)^2#
