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Factor completely. If the polynomial cannot be factored, say it is prime.
x^6 + 2x^3 + 1
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We're in luck here because (x^3)^2 = x^6
So substitute Y = x^3 and you'll get a quadratic in Y.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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Bob,
Thank you. You said we're in luck in this case because (x^3)^2 = x^6.
What if the question is not so obvious? What then?
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Factor completely. If the polynomial cannot be factored, say it is prime.
x^6 + 2x^3 + 1
We're in luck here because (x^3)^2 = x^6
You said we're in luck in this case because (x^3)^2 = x^6.
What if the question is not so obvious? What then?
then maybe it cant be factored, right?
if your doing perfect sqares then it has to fit into perfect aquare pattern
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We're in luck here because (x^3)^2 = x^6
So substitute Y = x^3 and you'll get a quadratic in Y.
Bob
Let me see.
Rewrite x^6 as (x^3)^2.
Let u = x^3
u^2 + 2u + 1
Factor.
(u + 1)(u + 1)
Back-substitute for u.
(x^3 + 1)(x^3 +1)
The sum of cubes tells me that (x^3 + 1) is the same thing as
(x + 1)(x^2 - x + 1).
My answer is (x + 1)(x^2 - x + 1)^2.
Textbook answer is (x + 1)^2(x^2 - x + 1)^2.
Who is right and why?
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Rewrite x^6 as (x^3)^2.
Let u = x^3
u^2 + 2u + 1
Factor.
(u + 1)(u + 1)
Back-substitute for u.
(x^3 + 1)(x^3 +1)
The sum of cubes tells me that (x^3 + 1) is the same thing as
(x + 1)(x^2 - x + 1).My answer is (x + 1)(x^2 - x + 1)^2.
Textbook answer is (x + 1)^2(x^2 - x + 1)^2.
Who is right and why?
in the red part you have
in the blue part you factored
then replace
the aquare goes on both factors inside
once you do that youll match the books answer
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Thank you.
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