Question

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

Answer 1

1. Get all possible numerators of rational zeros by listing all the possible divisors of the absolute value of the constant term. In this case the constant term is -4. It's absolute cvalue is 4. The divisors of 4 are 1,2, and 4, since they are the only integers which divide evenly into 4. 2. Get all possible denominators of rational zeros by listing all the possible divisors of the coefficient of the largest power of x. In this case the term with the largest power of x is 9x^5 and the absolute value of its coefficient is 9. The divisors of 9 are 1,3, and 9, since they are the only integers which divide evenly into 4. 3. Make all possible fractions having a numerator from the set of possible numerators and a denominator from the set of possible denominators. In this case that would be , , , , , , , , 4. Reduce them, and remove any duplications (sometimes there are duplications, there just aren't any here). 1, , , 2, ,, 4, , 5. Give them both signs, + and - ±1, , , ±2, ,, ±4, , ------------------------------------------------ Find all real zeros of the function. g(x)= x^3 + 4x^2 - x - 4 We don't even need the above method to do this one because it can be factored by grouping: g(x) = x³ + 4x² - x - 4 g(x) = x²(x + 4) - 1(x + 4) g(x) = (x + 4)(x² - 1) g(x) = (x + 4)(x - 1)(x + 1) So the zeros are found by setting all the factors = 0 x + 4 = 0, x - 1 = 0, x + 1 = 0 x = -4, x = 1, x = -1 Edwin