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

2 Answers
Aug 11, 2018

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

(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)