How do you factor #5x^4 + 2x^2 - 7#?

2 Answers
Aug 11, 2018

Answer:

#5x^4+2x^2-7=(x+1)(x-1)(5x^2+7)#

Explanation:

#5x^4+2x^2-7=5x^4+7x^2-5x^2-7#
because,

#7 xx -5 = -35#

#7 + (-5) = 2#

#=x^2(5x^2+7)-1xx(5x^2+7)#

#=(x^2-1)xx(5x^2+7)#

Further,

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

Thus,

#5x^4+2x^2-7=(x+1)(x-1)(5x^2+7)#

Aug 11, 2018

Answer:

#(x-1)(x+1)(5x^2+7)#

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)#