# 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)#