Extend polynomial identities to complex numbers, such as factoring sums of squares over the complex numbers.
Compare separate real and complex linear factorizations
Problem
For \(x^{2}+9\), determine whether real linear factors exist from its discriminant or roots. Then factor it into linear factors over \(ℂ\) and state the field comparison.
Big Picture
What this problem is really about
Whether a polynomial has linear factors depends on the coefficient field. We’ll use the discriminant to rule out real roots, solve for the complex conjugate roots, build their linear factors, and state the contrast between real and complex factorizations without changing the polynomial.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
