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In this activity you will learn about the Rational Root Theorem. The Rational Root Theorem gives an algebraic method for determining possible rational roots of a polynomial function. Recall that a rational number is any number that can be written as a fraction or terminating decimal. In Part I of this lesson, you will be working your way throughslides. Take notes as you go. Hit "OK" to get to the next slide. In this activity you will learn about the Rational Root Theorem. The Rational Root Theorem gives an algebraic method for determining possible rational roots of a polynomial function. Recall that a rational number is any number that can be written as a fraction or terminating decimal. Classify each number. √5 0.23 Irrational ? Rational ? The roots/zeros/solutions of a polynomial functionare the x-intercepts of the function. Consider the function: y = x2 – 2x – 3. The roots/zeros/solutions of a polynomial functionare the x-intercepts of the function. Consider the function: y = x2 – 2x – 3. The roots can be found by solving this equation: x2 - 2x - 3 = 0 (x – 3)(x + 1) = 0 x = –1, x = 3 are the roots. The roots/zeros/solutions of a polynomial functionare the x-intercepts of the function. Consider the function: y = x2 – 2x – 3. The roots can be found by solving this equation: Check by graphing the function! x2 - 2x - 3 = 0 (x – 3)(x + 1) = 0 x = –1, x = 3 are the roots. Note: If a polynomial function passes through the x-axis, the points of intersection are the "real" roots. Real roots can be either rational or irrational. In this lesson, we are interested in finding *rational* roots. Find the roots! The Rational Root Theorem gives us a list of all of the*possible* rational roots of a polynomial. Given the polynomial function: y = 5x3-7x2-5x+7 1. Write a fraction bar. 2. List all factors of the constant termin the numerator The Rational Root Theorem gives us a list of all of the*possible* rational roots of a polynomial. Given the polynomial function: y = 5x3-7x2-5x+7 1. Write a fraction bar. 2. List all factors of the constant termin the numerator The rational root theorem gives us a list of all of the*possible* rational roots of a polynomial. Given the polynomial function: y = 5x3-7x2-5x+7 ±1, ±7 1. Write a fraction bar. 2. List all factors of the constant termin the numerator3. List all factors of the leadingcoefficient in the denominator The rational root theorem gives us a list of all of the*possible* rational roots of a polynomial. Given the polynomial function: y = 5x3-7x2-5x+7 ±1, ±7 1. Write a fraction bar. 2. List all factors of the constant termin the numerator3. List all factors of the leadingcoefficient in the denominator The rational root theorem gives us a list of all of the*possible* rational roots of a polynomial. Given the polynomial function: y = 5x3-7x2-5x+7 ±1, ±7 ±1, ±5 1. Write a fraction bar. 2. List all factors of the constant termin the numerator3. List all factors of the leadingcoefficient in the denominator4. List all combinations of quotients. These are the possible rational roots. The rational root theorem gives us a list of all of the*possible* rational roots of a polynomial. Given the polynomial function: y = 5x3-7x2-5x+7 ±1, ±7 ±1, ±5 1. Write a fraction bar. 2. List all factors of the constant termin the numerator3. List all factors of the leadingcoefficient in the denominator4. List all combinations of quotients.These are the possible rational roots The rational root theorem gives us a list of all of the*possible* rational roots of a polynomial. Given the polynomial function: y = 5x3-7x2-5x+7 {1, -1, 7, -7, 1/5, -1/5, 7/5, -7/5} ±1, ±7 ±1, ±5 Write an expression that represents all possible rationalroots of the polynomial function. y = 3x3 - 5x2 + x - 4 Factors of -4 ? Factors of 3 ? Write an expression that represents all possible rationalroots of the polynomial function. y = 3x3 - 5x2 + x - 4 Factors of -4 Factors of 3 ± ± 1, 2, 4 ? 1, 3 ? How do we know which numbers on the list are actually zeros/roots/solutions? There are three ways. How do we know which numbers on the list are actually zeros/roots/solutions? There are three ways. How do we know which numbers on the list 1. Plug In/ Evaluate the function are actually answers/roots/solutions? There are three ways. How do we know which numbers on the list 1. Plug In/ Evaluate the function 2. Divide using synthetic division are actually answers/roots/solutions? There are three ways. How do we know which numbers on the list 1. Plug In/ Evaluate the function. 2. Divide using synthetic division 3. Graph the related function are actually answers/roots/solutions? There are three ways. How do we know which numbers on the list If the value of the function is zero using any of these threemethods, then the number is a root of the function! 1. Plug In/ Evaluate the function. 2. Divide using synthetic division 3. Graph the related function are actually answers/roots/solutions? |