Answer
(-infinity, $-5)$ U $(-1, 1)$ U $(5$, infinity)
Work Step by Step
$x^4-26x^2+25\geq0$
$x^4-25x^2-x^2+25 \geq 0$
$x^2(x^2-25)-1(x^2-25)\geq 0$
$(x^2-1)(x^2-25)\geq 0$
$(x+1)(x-1)(x-5)(x+5)\geq 0$
$(x+1)(x-1)(x-5)(x+5)= 0$
$x+1=0$
$x=-1$
$x-1=0$
$x=1$
$x-5=0$
$x=5$
$x+5=0$
$x=-5$
(-infinity, $-5)$
$(-5, -1)$
$(-1, 1)$
$(1, 5)$
$(5$, infinity)
Let $x=-10$, $x=-3$, $x=0$, $x=3$, $x=10$
$x=-10$
$(x+1)(x-1)(x-5)(x+5)\geq 0$
$(-10+1)(-10-1)(-10-5)(-10+5)\geq 0$
$-9*-11*-15*-5 \geq 0$
$7425 \geq 0$ (true)
$x=-3$
$(x+1)(x-1)(x-5)(x+5)\geq 0$
$(-3+1)(-3-1)(-3-5)(-3+5)\geq 0$
$-2*-4*-8*2 \geq 0$
$-128 \geq 0$ (false)
$x=0$
$(x+1)(x-1)(x-5)(x+5)\geq 0$
$(0+1)(0-1)(0-5)(0+5)\geq 0$
$1*-1*-5*5 \geq 0$
$25 \geq 0$ (true)
$x=3$
$(x+1)(x-1)(x-5)(x+5)\geq 0$
$(3+1)(3-1)(3-5)(3+5)\geq 0$
$4*2*-2*8 \geq 0$
$-128 \geq 0$ (false)
$x=10$
$(x+1)(x-1)(x-5)(x+5)\geq 0$
$(10+1)(10-1)(10-5)(10+5)\geq 0$
$11*9*5*15 \geq 0$
$7425 \geq 0$ (true)
