Precalculus · Problem 3.3.30
Polynomial Functions — Stitz & Zeager
Mathematics — Precalculus · finding-real-zeros-polynomials
Problem
Find the real zeros of the polynomial using the techniques specified by your instructor. State the multiplicity of each real zero.Intuitive explanation
The key is to recognize that this polynomial has a hidden structure—try grouping terms in pairs to factor out common expressions. Once you spot a repeated factor, you'll unlock both the zeros and their multiplicities without needing the rational root theorem or synthetic division. Look for a pattern where the same binomial appears more than once after factoring each group.
Intuitive explanation
The key is to recognize that this polynomial has a hidden structure—try grouping terms in pairs to factor out common expressions. Once you spot a repeated factor, you'll unlock both the zeros and their multiplicities without needing the rational root theorem or synthetic division. Look for a pattern where the same binomial appears more than once after factoring each group.