  ### WHAT DO YOU CALL A HUNGRY PARROT? - Polly, no meal

Polynomials are expressions composed of terms.

Polynomials include binomials (expressions with two terms) and trinomial (expressions with three terms) and each of these are also considered polynomials (expressions with many terms). Some consider monomials (expressions with only 1 term) as polynomials though mono, one, does not mean poly, many.

To ADD polynomials which are like, one combines like terms -- factor and simplify or add the coefficients and copy the bases and their exponents. To SUBTRACT polynomials which are like, one distributes the negative and combines like terms.   [So an expression like (4x - 2) - (3x + 1) becomes 4x -2 - 3x - 1, then x - 3.]

MULTIPLICATION of polynomials works like multiplication of constants -- each term of one factor polynomial is multiplied by each term of the other factor polynomial, then, like terms are combined.

 Multiply: 234(51)234x51----------- 234 1170  ------------11934 Multiply: (2x2+3x+4)(5x+1) 2x2+3x+45x+1--------------------- 2x2+3x+4 10x3+15x2+20x    ----------------------------- 10x3+17x2+23x+4

To SQUARE means to use the expression to be squared as a factor twice, perform the multiplication, then combine like terms. [The expression (x+3)2 becomes (x+3)(x+3), becomes x2 +3x + 3x + 9, becomes x2 + 6x + 9.

To CUBE means to use the expression to be cubed as a factor three times, perform the multiplication, then combine like terms.

The expression (x+3)3 becomes
(x+3)(x+3)(x+3), becomes
(x+3)(x2 +3x + 3x + 9), becomes
(x+3)(x2) + (x+3)(6x) + (x+3)(9), becomes
x3 +3x2 + 6x2 +18x + 9x+27, becomes
x3 +9x2 + 27x + 27.

To "FOIL" means to multiply two binomials, multiplying FIRST terms, then OUTER terms, then INNER terms, then LAST terms. To repeat the amination below, press REFRESH or RELOAD on your browser.. DIVISION of polynomials works much like division of constants. To "UNFOIL" means to reverse the multiplication by factoring. An animation of the factoring of 1x² + bx + c is provided here. Additional resources are listed below.

Resources
 Addition/Subtraction Computation Rules/Laws Know The Invisible (Understood) Ones. Combine Like Terms - Gives instructions and examples. Multiplication/Factoring Multiplying Two Binomials -- animation. Written Notes on Factoring SPECIAL PRODUCTS - multiplication and factoring VOCABULARY FOIL - Binomial Multiplication (animation) The Man With The Big Nose - the layout for the four multiplications required in multiplying 2 binomials Factor: 1x² + bx + c (animation) - when the leading coefficient is 1 Factor: ax² + bx + c Factoring Trinomials with A Leading Coefficient that Is Not One (animation) Written Notes on Factoring - Factoring Trinomials (animation) All Sorts of Stuff - Algebra Notes Vocabulary THE SENTENCE PLEASE! - writing algebraic phrases and statements EXPONENTS ARE NOT ON THE LEVEL - exponents, base, coefficients, monomial operations WHAT DO YOU CALL A HUNGRY PARROT? - polynomial operations and names IT'S THE LAW - distributive, inverses, identities, etc. SPECIAL PRODUCTS - multiplication and factoring RESOURCE PAGE - Special Products, Multiplication, Factoring RADICAL IDEAS - irrational numbers and roots VOCABULARY Quadratics Quadratic Equation - this page computes using the formula, & the discriminant A Family of Quadratics y = ax2 + bx + c Squaring, y = x2, y = x ·x What's a Function? - Index on topics like "How Functions Are Composed or Created", "Polynomial & Rational Functions" - Function and Relation Library - Many functions w/their features & graphs EVERYTHING YOU EVER WANTED TO KNOW ABOUT QUADRATICS BUT WERE AFRAID TO ASK Vocabulary - parabolas, quadratics Resources - Quadratic Equations, Formula, & The Discriminant