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Homework #4 Pre Calculus Due 9/30/08 Name: 1. Period Date: Factor the following quadratics (a) p( x) x 2 x 30 (b) p ( x) 4 x 2 5 x 6 How did you decide which numbers to try as factors? Did you use the Factor Theorem? How would you extend your thinking in 1 to factor higher order polynomials? 2. f ( x) x 4 3x3 15x 2 19 x 30 . If we were to factor this polynomial as ( x a)( x b)( x c)( x d ) , what would be the possible values of a, b, c and d? Given the polynomial Try to find the values of a, b, c, and d by using the Factor Theorem and dividing out each factor as you successfully find it. Graph the function on your calculator to check your answers. 3. The polynomial equation 3x 5 x 26 x 8 0 has a solution which is not an integer, but it is a rational number. To use your calculator to help you find the solutions in such a case, set the xscl to 1/3. (Why would we do this?) Set the window to: Xmin = -5 Ymin = -20 Xmax = 5 Ymax = 60 Xscl = 1/3 Yscl = 1 3 2 If we look at the graph we see that it crosses the x-axis one notch to the right at x twelve notches to the left at 4. 1 , six notches to the right at x 2 , 3 x 4 . Write this equation in factored form and show that the factoring works. Use a similar technique to solve 2 x x 31x 15 0 (what is your x-step here?) 3 2 D:\840970165.doc 5. Use the rational roots theorem and the factor theorem to factor the following polynomials (you may use your calculator as much as you like) (a) x 3x 4 x 12 4 2 (b) 2 x 5 x 14 x 5 x 12 4 6. 3 2 Use the Remainder Theorem to solve the following. p ( x) x 3 x 2 x 5 . Find p (7) (a) Given (b) Given g x 3x 3 12 x 2 9 x 1 Find g ( 5) 7. What would the remainder be if 2 x134 7 x 45 x9 4 is divided by ( x 1) ? 8. Factor the following polynomials into products of linear and quadratic factors. Then, solve the equations. Your solutions may be complex numbers. (a) x 1 0 3 (b) x 16 0 4 9. Factor the following polynomials. For each one, note the kinds of zeros (complex, real, rational, irrational, or integer). (a) p ( x) x 4 2 x 2 1 (b) s ( x) x 3 3x 2 3x 2 D:\840970165.doc