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{ Intro to Polys

so cool

algebraic expression

consists of coefficients, variables, and exponents

x2 + 9

3p4q 2p3 + 12

6x5y3z + 2x2y2 5xy + y - 7

NO DIVISION!

NO FRACTIONAL EXPONENTS!

NO NEGATIVE EXPONENTS!

POLYNOMIAL

part of an algebraic expression

can be single number 4, 12, 77

variable x, y, z

product of variables and numbers x2y, 4p2q3, 2x

terms are separated by a + or a - 3x2 + 7x - 13

x5y3z + 3x2y2 - 3xy + y + 9

TERM

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greatest exponent for every term, add the exponents of each variable

the greatest sum is the degree of the polynomial

3x2 + 7x - 13 degree = 2

2p5 - 10p4 3p2 + 7 degree = 5

x5y3z + 3x2y2 3xy + y + 9 degree = 9

DEGREE

the number that comes before a variable

3x2y -12p5 2qr4 8z

leading coefficient

the coefficient connected to the term with the highest degree

3x2 + 7x - 13

2p5 - 10p4 3p2 + 7

_x5y3z + 3x2y2 3xy + y + 9

COEFFICIENT

a number on its own

3x2 + 7x - 13

2p5 - 10p4 3p2 + 7

_x5y3z + 3x2y2 3xy + y + 9

CONSTANT

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monomial: one term (NOT a poly)

5y -8x2 3

polynomial: sum of two or more terms binomial: sum of two terms

-3x2 + 2 9y8 2y x + 2

trinomial: sum of three terms

4x3 + 12x2 3x x2 + 3x + 9

Types of -nomials

highest degree first

3x2 7 + 4x3 + x6 becomes

x6 + 4x3 + 3x2 - 7

STANDARD (normal) FORM

4x5y3z + 3x2y2 y + 9

2pq + 3

x2 + y - 12

EXAMPLES