Polynomials and Equations

(a) Review of Factoring 

-          Factoring: the decomposition of a polynomial into products.

-          Types of Factoring: common, difference of squares/cubes, trinomial simple, trinomial normal, grouping and combination

(b)     Sum and Difference of Cubes/Squares 

a² – b² = (a+b)(a-b)

a² + b² = cannot be done

a³ – b³ = (a-b)( a²+ab+ b²)

a³ + b³ = (a+b)( a²-ab+ b²)

(c) Binomial Expansion Using Pascal’s Triangle

-          Procedure: write a “formula” derived from triangle.

-          Substitute

-          Simplify

(d)     Factor Theorem and Remainder Theorem.

Factor Theorem: if (x-a) is a factor of f(x), then f(a)=0

Remainder Theorem: if f(a) generates a non-zero value,t hen (x-a) is not a factor.

(e)     Factoring Methods:

a.       Quadratic Formulae

b.       Trinomial Formulae

c.       Completing the Square

d.       Substitution

e.       Factor Theorem

(f)       Word Problems: 

Remember to answer questions with a statement and to include proper units.

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