Show that the given values of c are zeros of P(x). P(x) = 2x4 − x3 − 14x2 − 5x + 6, c = −2, 1 2 To show that c = −2 is a zero of P(x), we first evaluate P(x) at x = −2. P(x) = 2x4 − x3 − 14x2 − 5x + 6 P(−2) = 2

0

4

− (−2)3 − 14(−2)2 − 5(−2) + 6 = 2

− (−8) − 14(4) − 5(−2) + 6

We have shown that P(−2)

. By the Factor Theorem, this means that x + 2 ---Select--- a factor of P(x), so −2 is a zero of P(x). To show that c = 1 2 is a zero of P(x), we first evaluate P(x) at x = 1 2 . P(x) = 2x4 − x3 − 14x2 − 5x + 6 P 

1 2

= 2

4

−

1 2 3

− 14

1 2 2

− 5

1 2

• 6 = 2

−

1 8

− 14

1 4

− 5

1 2

• 6 = We have shown that P 

1 2

= . By the Factor Theorem, this means that x − 1 2

---Select--- a factor of P(x), so 1 2 is a zero of P(x). Find all other zeros of P(x). (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities.) x =