Factor c^6-133c^3+1000

Math
c6-133c3+1000
Rewrite c6 as (c3)2.
(c3)2-133c3+1000
Let u=c3. Substitute u for all occurrences of c3.
u2-133u+1000
Factor u2-133u+1000 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 1000 and whose sum is -133.
-125,-8
Write the factored form using these integers.
(u-125)(u-8)
(u-125)(u-8)
Replace all occurrences of u with c3.
(c3-125)(c3-8)
Rewrite 125 as 53.
(c3-53)(c3-8)
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=c and b=5.
(c-5)(c2+c⋅5+52)(c3-8)
Simplify.
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Move 5 to the left of c.
(c-5)(c2+5c+52)(c3-8)
Raise 5 to the power of 2.
(c-5)(c2+5c+25)(c3-8)
(c-5)(c2+5c+25)(c3-8)
Rewrite 8 as 23.
(c-5)(c2+5c+25)(c3-23)
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=c and b=2.
(c-5)(c2+5c+25)((c-2)(c2+c⋅2+22))
Factor.
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Simplify.
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Move 2 to the left of c.
(c-5)(c2+5c+25)((c-2)(c2+2c+22))
Raise 2 to the power of 2.
(c-5)(c2+5c+25)((c-2)(c2+2c+4))
(c-5)(c2+5c+25)((c-2)(c2+2c+4))
Remove unnecessary parentheses.
(c-5)(c2+5c+25)(c-2)(c2+2c+4)
(c-5)(c2+5c+25)(c-2)(c2+2c+4)
Factor c^6-133c^3+1000

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