How do you factor #5x^4 + 2x^2 - 7#?
2 Answers
Aug 11, 2018
Explanation:
because,
Further,
Thus,
Aug 11, 2018
Explanation:
#"let "x^2=u#
#=5u^2+2u-7#
#"factor the quadratic using the a-c method"#
#"the factors of the product "5xx-7=-35#
#"which sum to "+2" are "-5" and "+7#
#"use these factors to split the middle term"#
#5u^2-5u+7u-7larrcolor(blue)"factor by grouping"#
#=color(red)(5u)(u-1)color(red)(+7)(u-1)#
#"take out the "color(blue)"common factor "(u-1)#
#=(u-1)(color(red)(5u+7))#
#"change u back to "x^2#
#=(x^2-1)(5x^2+7)#
#(x^2-1)" is a "color(blue)"difference of squares"#
#=(x-1)(x+1)(5x^2+7)#