Polynomials PDF

POLYNOMIA LS JERALD L. JALOS MAIN OBJECTIVES: BEFORE: You have simplified and evaluated algebraic expressions. Now: You will know which algebraic expressions are polynomials and which are not. Why? So you easily polynomials, identify their degree, and write them systematically. WHAT IS POLYN...

POLYNOMIA LS JERALD L. JALOS MAIN OBJECTIVES: BEFORE: You have simplified and evaluated algebraic expressions. Now: You will know which algebraic expressions are polynomials and which are not. Why? So you easily polynomials, identify their degree, and write them systematically. WHAT IS POLYNOMIALS? Special kinds of algebraic expressions. These are algebraic with many terms. From a latin word with prefix “poly” means many. Each term must not have a negative or fractional exponents in any of its variables. A term in a polynomial can be in the form “axn” or “ayn”, where a is any real number and n is a whole number. EXAMPLES: a real number a whole number ax n EXAMPLES: a = 7, a real number n = 2, a whole 7x number 2 EXAMPLES: a = -1, a real number: though 1 is not written in the expression, -y6 is also equal to -1y6 for 1 ia factor of any expression. n = 6, a whole -y 6 number Poly nomials can also have terms consisting of more than one variable. It must be in form of axnym where is any real number and n and m are whole numbers. x -4xy +y 2 2 NOTE: Remember that any variable with an exponent of zero is equal to 1. EXAMPLES: This expression is 1 not a polynomial 3 2 𝑦 because the 5 exponent of variable x is not whole number. Classifiaction of Polynomials Polynomials can be classified according to the number of their terms. MONOMIAL – a polynomial with only one term. Binomial – a polynomial with two terms. Trinomial – a polynomial with three terms. Multinomial – polynomial with more than three terms.  Kind of Examples Polynomial Monomial 11d, -pqr, 2(x+y) 3 Binomial a+b, x -1, 2 4m n – 7mn 3 3 Trinomial a -2a-15, 2 3 3 2  Identify the following whether it is Polynomial or Not Polynomial 1. e4 – 2e3 – 4e2 - 8e 2. a4 – 4a3b + 6a2b2 – 4ab3 + b4 3. -uv + 10 – u5v4 + u4v5 4. 9k-2 5. 27 – y-3 7. What is algebraic expression that have many terms? 8. What is polynomial that have more than three terms? 9. what is Latin word mean many? 10. What is polynomial that have only one term? TRUE or FALSE 1. Each term of polynomials must have fractional exponent on its variable. 2. Coefficient of each term must be a real numbers. 3. Exponent of each term must be a whole numbers. 4. Each term of must not have negative exponent. 5. The expression is not polynomials if the exponent is not a whole number.