MONOMIALS &POLYNOMIALS

MONOMIALSNUMERIC VALUES

OPERATIONSPOLYNOMIALS

NUMERIC VALUES (GRAPHING)OPERATIONSIDENTITIES

MONOMIALS

A monomial with variable x is the product of a real number by a non-negative integer

ax exponent

co-efficient variable The degree of a monomial in one variable

corresponds to the exponent of the variable. The degree of a monomial with many

variables is equal to the sum of the exponents.

n

NUMERIC VALUES

The numeric value of a monomial is obtained by replacing the variables by their corresponding given values.

3x - if x = 2, then 3 x (2) = 3 x 4 = 12.2 2

OPERATIONS

ADDING/SUBTRACTINGTwo monomials using the same variables,

each affected by the same exponents, are called “like terms”.

The sum of difference of two monomials that are “like terms” can be reduced to a single monomial.

Examples: 3x + 5x = 8x 5x y - 3x y = 2x y

2 2 2

2 3 2 3 2 3

OPERATIONS (cont’d)

To MULTIPLY/DIVIDE by a constant, multiply/divide the constant by the co-efficient

Ex. 5 x (3x ) = (5 x 3)x = 15x12x ÷ 3 = (12 ÷ 3)x = 4x

To MULTIPLY/DIVIDE by another monomial use the following procedure (Law of exponents)

Ex. 3x x 2x = 6x or -3x y x 5xy = -15x y

12x ÷ 6x = 2x

2 2 2

2 2 2

2 3 5 2 3 3 4

5 3 2

POLYNOMIALS

A polynomial in x is an algebraic expression formed by a monomial or the sum of monomials

P(x) = 3x - 2x + 5 polynomial with a single variable

P(x,y) = 2x y – 3xy + xy – 2x + 1 polynomial with two variables x and y

Binomial: 3x + 5x Trinomial: -2x + 3x – 1 Degree of a polynomial corresponds to the

highest degree of any of its monomials once reduced

2

2 2

2

2

NUMERIC VALUES (GRAPHING)

The numeric value of a polynomial is obtained by replacing the variables by their corresponding given values.

Example: a stone is thrown from the top of a 25m cliff, represented by H(t)=-5t + 20t + 25.

t= 3 sec: H(3)= -5(3 ) + 20(3) + 25 = - 45 + 60 + 25 = 40

“zero” of a polynomial is any value of the variable which makes the polynomial equal to zero H(5) = 0

2

2

NUMERIC VALUES (GRAPHING)cont’d

H(t) . (3,40) H(t) = - 5t +20t + 25

30 . (0,25)20

10 . (5,0)

0 t(s)

2

OPERATIONS

ADD/SUBTRACT:A(x) = 3x - 2x +5 and B(x) = 5x + 3x – 4

A(x) + B(x) = 8x + x + 1A(x) – B(x) = -2x - 5x + 9 MULTIPLY:3x (2x + 5x) = 6x + 15x(2x + 3)(5x – 2) = 2x(5x – 2) + 3(5x – 2)

= 10x - 4x + 15x – 6 = 10x + 11x = 6

2 2

2

2

2 3 5 3

2

2