MONOMIALS NUMERIC VALUES OPERATIONS POLYNOMIALS NUMERIC VALUES (GRAPHING) OPERATIONS IDENTITIES.

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MONOMIALS NUMERIC VALUES OPERATIONS POLYNOMIALS NUMERIC VALUES (GRAPHING) OPERATIONS IDENTITIES

 A monomial with variable x is the product of a real number by a non-negative integer ax exponent co-efficientvariable  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

 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 =

 ADDING/SUBTRACTING Two 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

 To MULTIPLY/DIVIDE by a constant, multiply/divide the constant by the co-efficient Ex. 5 x (3x ) = (5 x 3)x = 15x 12x ÷ 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

 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

 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 t= 3 sec: H(3)= -5(3 ) + 20(3) + 25 = = 40  “zero” of a polynomial is any value of the variable which makes the polynomial equal to zero H(5) = 0 2 2

H(t). (3,40) H(t) = - 5t +20t (0,25) (5,0) 0t(s) 2

 ADD/SUBTRACT: A(x) = 3x - 2x +5 and B(x) = 5x + 3x – 4 A(x) + B(x) = 8x + x + 1 A(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 =