How do you factor (10x+24)^2−x^4?

yongenelowk 2022-08-13 Answered
How do you factor ( 10 x + 24 ) 2 x 4
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Answers (1)

Evelin Castillo
Answered 2022-08-14 Author has 12 answers
(1) a 2 b 2 = ( a + b ) ( a b )
may be directly applied to
(2) ( 10 x + 24 ) 2 x 4
and we obtain
(3) ( 10 x + 24 ) 2 x 4 = ( 10 x + 24 + x 2 ) ( 10 x + 24 x 2 ) ;
but 10 x + 24 + x 2 and 10 x + 24 x 2 can be factored as well! We have
(4) 10 x + 24 + x 2 = ( x + 4 ) ( x + 6 ) ,
Apparently ( 10 x + 24 ) 2 x 4 may be completely reduced over Z [ x ] to linear factors:
(6) ( 10 x + 24 ) 2 x 4 = ( x + 4 ) ( x + 6 ) ( x + 2 ) ( x 12 ) ,
and its roots are −6,−4,−2 and 12. Cute, the way 10 x + 24 is always a perfect square for any of these integers; but, then again, that's factoring in Z [ x ] for you.
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