1. M3D17 Have out: Bellwork: pencil, red pen, highlighter, GP notebook
1. Write a standard (expanded) form equation of a quartic polynomial with the zeros
6i and
2. Find the polynomial P(x) whose graph is given.
(0, 6) y
total:

2. 1. Write a standard (expanded) form equation of a quartic polynomial with the zeros 6i and .
Bellwork: +1 +1 +½ +½ +½ +½ +1 +1
P(x) = (x2 – 5)(x2 + 36) +1
P(x) = x4 + 36x2 – 5x2 – 180
P(x) = x4 + 31x2 – 180 +1 +1 +1 +1

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

4. Possible rational zeros
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 p
a) P(x) = 2x3 – 9x2 + 27
Possible rational zeros
factors of 27
±1,
±3,
±9,
±27
make combinations…
factors of 2
±1, ±2 3
try x = ____ 2 –9 27
–18 –3 +6 –9
–27 –6 3 3 2 –3 –9  x
– 3
P(x) = 2x
2x2
–6x
P(x) =
+ 3
+ 3x –9

5. P(x) = 2x3 – 9x2 + 27 y P(x) = (x – 3)(2x2 – 3x – 9)
(0, 27)
0 = (x – 3)(x – 3)(2x + 3)
x – 3 = 0
2x + 3 = 0
x = 3
2x = –3
double zero
x = –1.5 x
(–1.5, 0)
(3, 0)
–1.5, 3, 3
x = _________

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