1. 2.6 Solving Polynomial Equations

2. Ex 1) Find the zeros: f (x) = –3x4 + 18x3 – 27x2
Now that we are pros at solving quadratics, we will raise the bar &
solve any polynomial equation
- Remember answers can be real & non-real
- We will utilize our factoring skills & use the quadratic formula
Note: the largest power of x indicates how many answers/ zeros/ roots
the equation will have
- Each equation is a tad bit different: just use your skills! 
Ex 1) Find the zeros: f (x) = –3x4 + 18x3 – 27x2
0 = –3x4 + 18x3 – 27x2
0 = –3x2(x2 – 6x + 9)
0 = –3x2(x – 3)2
x = 0, 3
(but you need 4 answers!)
so… 0(mult 2), 3(mult 2)

3. Ex 2) Find the zeros: f (x) = 4x7 – 49x5
x = 0 (mult 5),
Ex 3) Solve: g(x) = 3x4 – 147
0 = 3x4 – 147
0 = 3(x4 – 49)
0 = 3(x2 – 7)(x2 + 7)
x2 – 7 = 0
x2 + 7 = 0
x2 = 7
x2 = –7

4. Reminder: Sum/ Diff of Cubes a3 – b3 = (a – b)(a2 + ab + b2)
Ex 4) Solve: f (x) = x6 + 7x3 – 8
Song! 
0 = x6 + 7x3 – 8
0 = (x3 – 1)(x3 + 8)
0 = (x – 1)(x2 + x + 1)(x + 2)(x2 – 2x + 4)
(quad form!)
(quad form!) 1 –2

5. Ex 5) Solve: 27x3 – 9x2 – 3x +1 = 0
9x2 (3x – 1)
– 1(3x – 1) = 0
(9x2 – 1)(3x – 1) = 0
(3x + 1)(3x – 1)(3x – 1) = 0
Ex 6) Use a graphing calculator to approximate the real zeros of the function to the nearest hundredth.
P(x) = 4x4 + 3x3 – 2x – 1
Just like before: 2nd CALC :zero
–0.57, 0.75

6. Homework
#207 Pg 97 # 1–29 odd, 30, 31, 33, 35, 38