Factor completely each polynomial, and indicate any that are not

sputneyoh 2021-12-14 Answered
Factor completely each polynomial, and indicate any that are not factorable using integers. x4+6x2+9
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Expert Answer

Fasaniu
Answered 2021-12-15 Author has 46 answers

Step 1
The given polynomial is x4+6x2+9
Step 2
Let x2=t we have
x4+6x2+9=t2+6t+9
=t2+3t+3t+9
=t(t+3)+3(t+3)
=(t+3)(t+3)
=(t+3)2
Resubstituting t=x2 we have
(t+3)2=(x2+3)2
Factors of given equation is
x4+6x2+9=(x2+3)(x2+3)
Solving the equation we get'
(x2+3)2=0
(x2+3)=0
x2=3
x=3
Therefore, no real solutions possible for given equation

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