1 polynomialfunction.pdf
- 1. POLYNOMIALS
- 3. OBJECTIVES At the end of the lesson, the students should be able to: 1. Recall the concepts of polynomial expression. 2. Illustrate a polynomial function. 3. Find the degree and the leading term of a polynomial function.
- 4. Review: Polynomials Polynomial Expression anXn +an-1Xn-1+ an-2Xn-2 + …+ a1X + a0 Polynomial Equation anXn +an-1Xn-1+ an-2Xn-2 + …+ a1X + a0 = 0 Polynomial expression Polynomial equation
- 5. ACTIVITY 1 – Which is which? Determine whether each of the following is a polynomial expression or not. On your miniboards write Y is the expression is polynomial; x if it is not a polynomial. Give reasons.
- 6. ACTIVITY 1 – Which is which?
- 7. POLYNOMIAL FUNCTIONS CONDITIONS: 1. Each exponent is a whole number. 2. Denominators contain no variable in x. 3. No variable is under the radical sign.
- 8. A polynomial function is a function of the form: ( ) o n n n n a x a x a x a x f + + + + = − − 1 1 1 All of these coefficients are real numbers n must be a positive integer The degree of one variable polynomial is the largest power on any x term in the polynomial. an ≠ 0
- 9. POLYNOMIAL FUNCTIONS ( ) o n n n n a x a x a x a x f + + + + = − − 1 1 1 leading term leading coefficient constant term
- 10. 1. f(x) = anXn an-1Xn-1+ an-2Xn-2 + …+ a1X + a0 POLYNOMIAL FUNCTION • an is called the leading coefficient • n is the degree of the polynomial • a0 is called the constant term *Standard Form – polynomials are written in descending powers of x. Polynomial function can be written in different ways: 2. y = anXn an-1Xn-1+ an-2Xn-2 + …+ a1X + a0 y = x4 + 2x3 –x2 +14x – 56 in factored form is y = (x2 + 7)(x -2 )(x + 4)
- 11. Examples: 1.) f(x) = 2x3 – 10x + x4 – 13x2 Standard form: Degree: Leading Coefficient: Constant Term: 2.) y = -45 + 45x2 + 66x + 6x3 Standard form: Degree: Leading Coefficient: Constant Term: POLYNOMIAL FUNCTION f(x) = x4 + 2x3 – 13x2 – 10x 4 1 0 f(x)=6x3 + 45x2 + 66x - 45 3 6 -45
- 12. Polynomial Functions Polynomial Function in General Form Degree Name of Function 1 Linear 2 Quadratic 3 Cubic 4 Quartic The largest exponent within the polynomial determines the degree of the polynomial. e dx cx bx ax y + + + + = 2 3 4 d cx bx ax y + + + = 2 3 c bx ax y + + = 2 b ax y + =
- 13. ACTIVITY 2 – Fix and Move Them, then Fill Me Up