Math III · N-CN.9

Know the Fundamental Theorem of Algebra and connect it to polynomial roots.

Know the Fundamental Theorem of Algebra and connect it to polynomial roots.

Concept Number and Quantity
Domain The Complex Number System
Problem Types

Problem Templates In This Objective

10 problem types are attached to this objective. The full web app handles practice, answers, hints, and walkthroughs.

Template 1

Determine the total number of complex roots of a polynomial from its degree

4 variants
Template 2

Count the complex roots of a factored polynomial, including multiplicity

4 variants
Template 3

Find missing polynomial roots from the degree, counting multiplicity

4 variants
Template 4

Find the conjugate root of a real-coefficient polynomial

4 variants
Template 5

Build the monic polynomial from roots and multiplicities

4 variants
Template 6

Connect root records to visible graph behavior

4 variants
Template 7

Evaluate and classify a real or complex root candidate

4 variants
Template 8

Infer the minimum number of nonreal roots from a polynomial graph and its degree

4 variants
Template 9

Enumerate polynomial root structures by degree slots

4 variants
Template 10

Relate concrete complete factorizations over R and C

4 variants