Unit 2 Factors & Polynomials (chapter 3 of the textbook)
In this section, students will be expected to classify polynomials by type and order, simplify polynomial expressions gathering like terms and expressing the polynomial in decreasing order of variables. Students will be introduced to several expansion (multiplying) techniques including the use of algebraic tiles, algebraic expansion (including FOIL) and the supplemental long multiplication technique for large polynomials.
The second half of this unit extends the concept of factoring numbers and monomials to factoring larger polynomial expressions. Factoring polynomials is the process breaking or splitting a polynomial into smaller polynomial expressions that when multiplied together result in the original polynomial. This process is described as the opposite function of multiplying polynomials and students are shown both how to divide polynomials and also use algebraic tiles to graphically illustrate the factoring process for simple quadratic polynomials. Algebraic factoring techniques covered include common monomial factors, special factors (such as differences of squares and perfect trinomial squares) and basic trinomial factoring (such as the Inspection and Decomposition techniques). Lastly, students will extend the concepts of factors to include polynomial Greatest Common Factors (GCF) and Lowest Common Multiples (LCM).
note: Operations on polynomials and polynomial factoring are core components in both math 20-1 and math 30-1. Students wishing to proceed to math 20-1 and 30-1 require a strong understanding of these core components.
In this section, students will be expected to classify polynomials by type and order, simplify polynomial expressions gathering like terms and expressing the polynomial in decreasing order of variables. Students will be introduced to several expansion (multiplying) techniques including the use of algebraic tiles, algebraic expansion (including FOIL) and the supplemental long multiplication technique for large polynomials.
The second half of this unit extends the concept of factoring numbers and monomials to factoring larger polynomial expressions. Factoring polynomials is the process breaking or splitting a polynomial into smaller polynomial expressions that when multiplied together result in the original polynomial. This process is described as the opposite function of multiplying polynomials and students are shown both how to divide polynomials and also use algebraic tiles to graphically illustrate the factoring process for simple quadratic polynomials. Algebraic factoring techniques covered include common monomial factors, special factors (such as differences of squares and perfect trinomial squares) and basic trinomial factoring (such as the Inspection and Decomposition techniques). Lastly, students will extend the concepts of factors to include polynomial Greatest Common Factors (GCF) and Lowest Common Multiples (LCM).
note: Operations on polynomials and polynomial factoring are core components in both math 20-1 and math 30-1. Students wishing to proceed to math 20-1 and 30-1 require a strong understanding of these core components.
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M10C Standards Unit 3 Exponents & Radicals.pdf | |
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Basic Tutorials on Polynomials:
The first set of videos look at classifying polynomials, simplifying polynomials and basic operations on polynomials.
Classifying and Simplifying Polynomials
The first set of videos look at classifying polynomials, simplifying polynomials and basic operations on polynomials.
Classifying and Simplifying Polynomials
Operations on Polynomials
Enrichment / Optional Material
An extension for those you who want to be challenged is called Synthetic Division. Synthetic Division evolved from long division of polynomials about two hundred years ago to division by detached coefficient and eventually was simplified to the the following technique. |
Synthetic Division can represent a division either by a divisor in the form (x - a) or as a division by the root, zero, solution or x-intercept of a polynomial function in the form x = a.
Synthetic Division appears in Math 30-1 as a complementary method for simplifying complex polynomial functions. |
Basic Tutorials on Several Factoring Polynomial Techniques
A substantial portion of all algebraic work from this point on through to the completion of high school requires students to demonstrate a strong understanding of basic polynomial factoring.
Enrichment / Optional Material
In addition to the above basic factoring techniques, here are some additional methods that can be used to break larger polynomial and more complex polynomials into factors.
In addition to the above basic factoring techniques, here are some additional methods that can be used to break larger polynomial and more complex polynomials into factors.
Additional Variations For Factoring Quadratic Polynomials
Here are a couple of different ways to look at factoring quadratic trinomials. The top row looks at a common method known as "The Box method" while the bottom row covers other variations of this factoring technique.
Some food for thought...
Join Jason Silva every week as he freestyles his way into the complex systems of society, technology and human existence and discusses the truth and beauty of science in a form of existential jazz.
This video is called "We Need To Be Lost To Find Ourselves" |
Published on Mar 3, 2015"
Artists are uniquely placed to ... creatively participate in the larger cultural process of re-engineering subjectivity, of pushing the envelope of experience." - Erik Davis |