The polynomial p(x)=((x−1)^2 −2)^2 +3 can be fully factored into first-order terms by solving the equation ((x−1)^2 −2)^2 +3 = 0. This results in four complex roots, which can be determined by isolating (x−1)^2 and taking the square root of both sides. The process involves identifying the two solutions for ((x−1)^2 −2) and subsequently solving for x to find all complex roots.
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Solve \displaystyle ((x−1)^2 −2)^2 +3 = 0 in steps.hoopsmax25 said:Homework Statement
p(x)=((x−1)^2 −2)^2 +3. From here find the full factorization of p(x) into the product of first order terms and identify all the
complex roots.
Homework Equations
I am having trouble doing this by hand. I know there are four complex roots but can't seem to figure out how to get them factored out.
The Attempt at a Solution