JEOPARDY X

Sequence

100

10th term in the Fibonacci Sequence

55

200

1,2,4,_,_,32

8 & 16

300

1,2,3,_,_,_,7

4,5 & 6

400

2,__,8,__,14,__20

5,11,17

500

2,4,__,__,__,__,128,__

8,16,32,64,256

Synthetic Division

100

 2x²+ x by x - 1

 Q = 2x + 3 , R = 3

200

7x⁵- 2x⁴ - 5x³ + x² - 3x + 5 by x - 2

Q = 7x⁴ + 12x³ + 19x² + 39x + 75, R = 155

300

(1/2)x³ - (1/3)x² - (3/2) x + 1/3 by x - 1/2

Q = (1/2)x² - (1/2)x - 37/24 , R = -7/16

400

(x⁴-3x³+x²+4x-5) ÷ (x²+x-2)

1,-4,7,11,9

∴ x⁴-3x³+x²+4x-5=(x²x-2)(x²-4x+7)-11x+9

500

(x⁶+x⁴+2x²-828) ÷ (x-3)

1,3,10,30,92,276,0

Thus,

(x⁶+x⁴+2x²-828) ÷ (x-3)=

x⁵+3x⁴+10x³+30x²+92x+276

Remainder Theorem

100

P(x)=x² + 3x – 11

D(x)=x – 2

 -1

200

 P(x)=x⁴ – 2x³ – x² + 2x – 2 

D(x)= x – 4

118

300

P(x)= x⁴ – x³ – x² – x – 1 

D(x)= x – 3

41

400

P(x)=3x³-2x²+x-6

D(x)=x-4

158

500

P(x)=x⁶+4x⁵+9x³-4x²+10

D(x)=x+1

-6

Possible Roots

100

P(x)=2x²-3x²-11x+6

± 1,± 1/2,± 1/3,± 1/6,± 2,± 1/3,± 2/3 

200

P(x)=6x⁴-2x³+5x²+x-10

± 1,± 1/2 ,± 1/5,± 1/10,± 2,± 2/5,± 5,± 5/2

300

P(x)=6x³+31x²+4x-5

± 1,± 1/2,± 1/3,± 1/6,± 5,± 5/2,± 5/3,± 5/6

400

x³+x²+6=0

±1,± 2,±3,±6

500

2x³+12x²+16x+6=0

±1,±2,±3,±,±1/2,±3/2