Question

Choose the correct answer from the alternative given.
The factors of ($x^4$$-625)$are

• A. $(x^2-25)(x^2+25)$
• B. $(x^2+25)(x^2+25)$
• C. $(x^2-10x+25)(x^2+5x+24)$
• D. ($x^2$ $+25\left)\right(x+5\left)\right(x-5)$

Answer 1

Answer: (D)

($x^2$ $+25\left)\right(x+5\left)\right(x-5)$

$x^4$-625
$(x^2{)}^2$ - $(25{)}^2$ ; We know, ( $a^2-b^2)$ = (a + b) (a b)
$(x^2+25)(x^2-25)$
Rewriting $25$ as $5^2$
$=(x^2+25)$ $(x^2-(5{)}^2)$

$=(x^2$$+25\left)\right(x+5\left)\right(x-5)$