Write a linear factorization of the function. f(x) = x4 + 81x2
Answer:
\(f(x)= x^2(x+9i)(x-9i)\)
Step-by-step explanation:
\(f(x) = x^4 + 81x^2\)
Lets factor GCF x^2
\(f(x) =x^2(x^2+81)\)
Now factor out \(x^2+81\)
LEts find out factors by solving, set the parenthesis =0 and solve for x
\(x^2+81=0\)
Subtract 81 on both sides
\(x^2=-81\)
take square root on both sides
\(x^2=\sqrt{-81}\)
\(\sqrt{-1} =i\)
\(x=i\sqrt{81}\)
\(x=+-9i\)
Two roots are \(x=-9i , x=+9i\)
Factors are \((x+9i)(x-9i)\)
So \(f(x)= x^2(x+9i)(x-9i)\)