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Sagot :
we have the expression
x^4+6x^2−7
Note that, if you substitute for x=1
(1)^4+6(1)^2-7
1+6-7
7-7=0
that means
x=1 is a root of the given equation
(x-1) is a factor of the given equation
so
Divide x^4+6x^2−7 by (x-1)
x^4+6x^2−7 : (x-1)
x^3+x^2+7x+7
-x^4+x^3
---------------
x^3+6x^2-7
-x^3+x^2
---------------
7x^2-7
-7x^2+7x
-------------
7x-7
-7x+7
----------
0
therefore
x^4+6x^2−7=(x-1)(x^3+x^2+7x+7)
Note that in the cubic function, if you substitute for x=-1
(-1)^3+(-1)^2+7(-1)+7=0
so
x=-1 is a root of the cubic function
(x+1) is a factor
Divide x^3+x^2+7x+7 by (x+1)
x^3+x^2+7x+7 : (x+1)
x^2+7
-x^3-x^2
-------------------
7x+7
-7x-7
----------
0
so
x^3+x^2+7x+7=x^2+7
therefore
x^4+6x^2−7=(x+1)(x-1)(x^2+7)
the answer is
(x+1)(x-1)(x^2+7)
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