Statistics Mathematics

Name: _______________________ CW/HW Sec 3.4 thru 3.6 (5𝑥𝑥 4 − 3𝑥𝑥 3 + 2𝑥𝑥 2 − 1) ÷ (𝑥𝑥 2 + 4) 1. Divide using polynomial long division: 2. Use synthetic division to divide: (4𝑥𝑥 2 + 3𝑥𝑥 − 1) ÷ (𝑥𝑥 − 3) 3. Use the Remainder Theorem to indicate if 𝑥𝑥 3 + 4𝑥𝑥 2 − 5𝑥𝑥 + 5 is evenly divisible by x – 3. 4. Use the fact that P(3) = 0 to find the horizontal intercepts of 𝑃𝑃(𝑥𝑥) = 2𝑥𝑥 3 − 3𝑥𝑥 2 − 11𝑥𝑥 + 6 5. Find the other zeros for the polynomial using factoring. It is poor form to leave a polynomial factor to include a fraction; rewrite if necessary into an equivalent factor. 1 4𝑥𝑥 4 − 28𝑥𝑥 3 + 61𝑥𝑥 2 − 42𝑥𝑥 + 9, 𝑥𝑥 = 𝑤𝑤𝑤𝑤𝑤𝑤ℎ 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 2 2 Name: _______________________ CW/HW Sec 3.4 thru 3.6 6. Use Cauchy’s Bound to find an interval containing all real zeros and then use the Rational Roots Theorem to make a list of all possible rational zeros for: 𝑓𝑓(𝑥𝑥) = 2𝑥𝑥 4 + 𝑥𝑥 3 − 7𝑥𝑥 2 − 3𝑥𝑥 + 3 7. Find all the real zeros for the function in #6. 8. Find all the zeros of the polynomial and completely factor it over the real numbers. 𝑓𝑓(𝑥𝑥) = 4𝑥𝑥 4 − 4𝑥𝑥 3 + 13𝑥𝑥 2 − 12𝑥𝑥 + 3 9. Simplify each to a single complex number: a) √−6√−75 b) 4−√−20 2 c) (2 − 3𝑖𝑖) − (3 + 2𝑖𝑖) d) (−1 + 2𝑖𝑖)(−2 + 3𝑖𝑖) e) 6+4𝑖𝑖 𝑖𝑖 f) 3+4𝑖𝑖 2−𝑖𝑖 Name: _______________________ CW/HW Sec 3.4 thru 3.6