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##### Polynomials: The Rational Zero Test

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**Polynomials: The Rational Zero Test**The Rational Zero Test states that if a polynomial with real coefficients has rational zeros each will be on the following list: c/d, where c is a factor of the constant term and d is a factor of the leading coefficient. Example: Make a list of possible rational zeros of the polynomial, P(x) = 4x3 + 19x2 + 20x + 6. The constant term is 6. Its factors are 1, 2, 3 and 6. These are values of c. The leading coefficient is 4. Its factors are 1, 2, and 4. These are values of d.**Simplifying and removing duplicate fractions results in:**Polynomials: The Rational Zero Test c-values – 1, 2, 3 and 6 d-values – 1, 2 and 4 Now form all fractions of the form: c/d: Slide 2**The polynomial in the example,**(P(x) = 4x3 + 19x2 + 20x + 6) actually has three real zeros: Polynomials: The Rational Zero Test Two of the zeros are irrational; only one is rational (- 3/4). The Rational Zero Test makes no claims beyond those for rational zeros. It simply states that if any rational zeros exist, they will appear on the computed list. Indeed, - 3/4 was on the computed list! Slide 3**The possible rational zeros are:**Polynomials: The Rational Zero Test Try: Make a list of possible rational zeros of the polynomial, P(x) = 5x3 – 14x2 + 3x + 4. Slide 4**Polynomials: The Rational Zero Test**END OF PRESENTATION Click to rerun the slideshow.