pencil red pen highlighter GP notebook 1 Write

pencil, red pen, highlighter, GP notebook 1. Write a standard (expanded) form equation of a quartic polynomial with the zeros 6 i and. 2. Find the polynomial P(x) whose graph is given. y y total: (0, 6)

1. Write a standard (expanded) form equation of a quartic polynomial with the zeros 6 i and. +1 +1 +½ +½ +1 +1 P(x) = (x 2 – 5)(x 2 + 36) +1 P(x) = x 4 + 36 x 2 – 5 x 2 – 180 P(x) = x 4 + 31 x 2 – 180 +1 +1

2. Find the polynomial P(x) whose graph is given. +½ y +½ +1 +1 +1 y +1 (0, – 6) total: +2 +1 +1

1. For each polynomial, use the Rational Root Theorem to: (i) list all possible rational zeros, (ii) find all zeros, (iii) sketch a graph of y = P(x). q a) P(x) = 2 x 3 – 9 x 2 + 27 Possible rational zeros p factors of 27 factors of 2 make ± 1, ± 3, ± 9, ± 27 combinations… ± 1, ± 2 3 try x = ____ 2 3 2 – 9 0 27 +6 – 9 – 27 – 3 – 9 – 18 3 – 6 – 3 x – 3 P(x) = 2 x 2 x 2 – 6 x P(x) = +3 + 3 x – 9

P(x) = 2 x 3 – 9 x 2 + 27 P(x) = (x – 3)(2 x 2 – 3 x – 9) P(x) = (x – 3)(2 x + 3) y (0, 27) 0 = (x – 3)(2 x + 3) x– 3=0 2 x + 3 = 0 x=3 2 x = – 3 double zero x = – 1. 5, 3, 3 x = _____ (– 1. 5, 0) (3, 0) x

Clear your desk except for a pencil, highlighter, and a NON-GRAPHING calculator! After the quiz, work on the rest of the worksheet.