Is $5^2x^3-x^5 = x^3(x-5)(x+5)$ or $-x^3(5-x)(5+x)$

Question

Geogebra's Factor function says that

$5^2x^3-x^5$

is

$-x^3(x-5)(x+5)$

but from what I do, it is positive, $x^3(5+x)(5-x)$

Note the x isnt in the same position

Am I wrong?

Answer 1

Look: $$5^2x^3-x^5=x^3(5^2-x^2)=x^3(5-x)(5+x)x^3(-1)(x-5)(x+5)=-x^3(x-5)(x+5).$$

Answer 2

Your answer and Geogebra's answers are equivalent.

$x^3(5+x)(5-x)=-x^3(5+x)(x-5)=-x^3(x+5)(x-5)$.

They just factored out a negative out of $(5-x)$ in order to make it $-(x-5)$.

Answer 3

No, you're not wrong (but the title doesn't reflect the question): $$ 5^2x^3-x^5=x^3(5^2-x^2)=x^3(5-x)(5+x) $$ You can use $5-x=-(x-5)$ to rewrite it as $$ -x^3(x-5)(x+5) $$

Answer 4

$5^2x^3-x^5=x^3(5^2-x^2)=x^3(5-x)(5+x)=-x^3(x-5)(x+5)$