October 25, 2020

# Polynomial Factoring

## Integer GCF

The GCF (greatest common factor) of integers. There is a student version, an extended teacher version for a smooth and efficient lesson, and the flow chart may be obtained separately.

## Monomial GCF

The GCF (greatest common factor) of monomials with applications to polynomial factoring. There is a student version, an extended teacher version for a slick lesson, and the flow chart may be obtained separately.

Working with integer coefficients of quadratic trinomials to find integer roots as a prequel to factoring the quadratic trinomials with regrouping. This is the special case where the leading coefficient is unity, but the general case is no more difficult with this algorithm. Other schemes are special cases of this one. There is a student version, an extended teacher version for a slick lesson with “animated” flow charts, and the flow chart may be obtained separately.

“Animated” flow charts are used to teach the logic of factoring quadratic trinomials with integer roots. This is the special case where the leading coefficient is unity, but the general case is no more difficult with this algorithm that employs regrouping after splitting the linear term. Other schemes are special cases of this one. There is a student version, an extended teacher version for a slick lesson with “animated” flow charts, and the flow chart may be obtained separately.

## DOTS: Difference of Two Squares

The difference of two squares is introduced as a special case of quadratic trinomials with zero linear coefficient. The simplified case is reached by discovery and then extended to related cases. Student and teacher materials are available for download.

## Factor Completely

Includes such cases as when a GCF needs to be factored out before factoring the residual quadratic trinomial. Also includes cases where the one factor may be refactored using the difference of two squares. Student and teacher materials are available for download.

The graph of the quadratic function considering roots, zeros and the vertex using factored form and the TI-84 calculator. Student and teacher materials are available for download.

## Zeros

Zeros of a quadratic function from factored form and from the TI-84 calculator. Student and teacher materials are available for download. 