Investigate the Fundamental Theorem of Algebra and explore polynomial equations to determine the number of factors, the number of roots, and investigate multiplicity of roots.

Consider complex numbers, roots, and quadratic equations. Use the discriminate as a way to determine the nature of a quadratic's roots. Then discuss the similarities and differences between quadratics with two, one, or no real roots....

Using their Ti-Nspire to determine the solutions of parabolas, young scholars explore the concept of complex roots.  Students determine if parabolas have real or complex roots.  Young scholars determine the the axis of symmetry...

Working with imaginary numbers — this is where it gets complex! After exploring the graph of complex numbers, learners simplify them using addition, subtraction, and multiplication. 

Many learners find completing the square the preferred approach to solving quadratic equations. Class members combine their skills of using square roots to solve quadratics and completing the square. The resource incorporates a...

Students solve problems with complex numbers. In this algebra lesson, students factor complex numbers and simplify equations using DeMoivre's Theorem. They add, subtract, multiply and divide using negative roots.

A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...

Learners identify the end behavior of polynomial graphs. In this algebra lesson, students factor and solve quadratic and complex equations. They factor out negative roots and identify the real and imaginary parts of an equation.

The greater the degree, the more solutions to find! Individuals find the real solutions from a graph and use the Fundamental Theorem of Algebra to find the remaining factors. 

These four problems will guide your class through the idea behind the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots. Use the division algorithm and the definition of a zero/root of a...

Pupils convert quadratic functions from standard form to vertex form. In this algebra lesson, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor theorem.

High schoolers factor polynomials and linear functions and apply concepts of the fundamental theorem of algebra to solve problems. They graph their solutions and analyze the graph.