Solve [itex]\displaystyle ((x−1)^2 −2)^2 +3 = 0[/itex] 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
Factorization of a complex polynomial involves breaking down a polynomial expression into simpler factors. These factors can be either real or complex numbers.
Factorization of a complex polynomial is important because it allows us to solve equations and find the roots of a polynomial. It also helps us understand the behavior and properties of the polynomial function.
The methods used for factorization of a complex polynomial include finding common factors, grouping terms, using the difference of squares formula, and using the quadratic formula for higher degree polynomials.
A real factor of a polynomial is a factor that can be expressed as a real number, while a complex factor cannot be expressed as a real number and includes imaginary components.
Not all complex polynomials can be factorized into simpler factors. Some polynomials may have irrational or imaginary roots, making it impossible to factor them using real numbers. However, all complex polynomials can be factored using complex numbers.