Extend polynomial identities to complex numbers, such as factoring sums of squares over the complex numbers.
Factor an expression of the form \(A^2+B^2\) over the complex numbers
Problem
Let \(u=x-3\) and factor \(u^{2}+16\) over \(ℂ\) as conjugates. Substitute \(x-3\) back without changing its sign.
Big Picture
What this problem is really about
Treating the shifted expression as one unit keeps the factorization organized. We’ll substitute a temporary variable for the whole binomial, split the resulting sum of squares into conjugates, restore the unchanged shifted expression in both factors, and multiply back to verify.
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.
