Jeopardy - MATH EDITION

Factors of Polynomials

100

factor x³+ 27

= x³+3³

⁼ (x+3)(x²-3x+3²)

SOLUTION - (x+3)(x²-3x+9)

200

factor a³+125

= a³+5³

= (a+5) (a²-5a+5²)

SOLUTION - (a+5)(a²-5a+25)

300

factor 8x³+27

= (2x)³+3³

= (2x+3)(2²x²- 3*2x+3²)

SOLUTION - (2x+3)(4x²-6x+9)

400

factor -27u3+125

= -(27u³-125)

=-(3u-5)(3²u²+5*3u+5²)

SOLUTION - -(3u-5)(9u²+15u+25)

500

factor 63n³+54n²-105n-90

= 3(21n³+18n²-35n-30)

SOLUTION - 3(7n+6)(3n²-5)

Polynomial Operations

100

simplify (3m⁴-8m)+2m-4m⁴⁾

= 3m⁴-8m+2m-4m⁴

⁼ 3m⁴-6m-4m⁴

= 3m⁴-4m⁴-6m

SOLUTION - -m⁴-6m

200

simplify (5x³-5x-1)+(5x+6)

= 5x³-5x-1+5x+6

= 5x³-5x+5x- 1+6

= 5x³-1+6

SOLUTION- 5x³+5

300

simplify (6p-5p⁴)-(4p⁴+6p³+3p)

= 6p-5p⁴-(4p⁴+6p³+3p)

= 6p-5p⁴-4p⁴-6p³-3p

= 6p-9p⁴-6p³-3p

= -9p⁴-6p³+6p-3p

SOLUTION - -9p⁴-6p³+3p

400

simplify (4x⁴+8x²+8x³)+(8x³+4x-4)-(2x⁴+6+x²)

= 4x⁴+8x²+8x³+8x³+4x-4-(2x⁴+6+x²)

= 4x⁴+8x²+16x³+4x-4-(2x⁴+6+x²)

=4x⁴+8x²+16x³+4x-4-2x⁴-6-x²

⁼ 4x⁴-2x⁴+16x³+8x²-x²+4x-4-6

SOLUTION - 2x⁴+16x³+7x²+4x-10

500

simplify (2p³-7p²+8p⁴)+(4p³+3p+8p²)-(5p⁴-7-5p³)

= 2p³-7p²+8p⁴+4p³+3p+8p²-(5p⁴-7-5p³)

= -(5p⁴-7-5p³)+8p⁴+6p³+p²+3p

= -5p⁴+7+5p³+8p⁴+6p³+p²+3p

= -5p⁴+8p⁴+5p³+6p³+p²+3p+7

SOLUTION - 3p⁴11p¹+p²+3p+7

Arithmetic Sequence

100

1,3,5,7...?

a_n=a₁+(n-1)d

a₅=1+(5-1)2

a₅=5*2

a₅=10

200

12,24,36,48...?

a_n=a₁+(n-1)d

a₅=1+(5-1)12

a₅=5*12

a₅=60

300

72,144,216,288,360,720...?

a_n=a₁+(n-1)d

a₇=1+(7-1)72

a₇= 7*72

a₇= 504

400

what is the 56th term of 8,16,24,32,...?

a_n=a₁+(n-1)d

a₅₆= 1+(56-1)8

a₅₆= 56*8

a₅₆= 448

500

what is the 2,569th term of 83,166,249,332,415...?

a_n=a₁+(n-1)d

a_2,569= 1+(2,569-1)83

a_2,569= 2,569*83

a_2,569= 213,227

Absolute Value Inequalities

100

evaluate |x+2|<=4

x+2<=4

x<=4-2

x<=2

-(x+2)<=4

x+2>=-4

x>=-4-2

x>=-6

200

evaluate |-6b|<=60

-60<=-6b<=60

b<=10 and b>=-10

-10<=b<=10

300

evaluate |-8a-3|>11

-8a-3<-11 or -8a-3>11

a<-(7/4) or a>1

400

evaluate 9|x+8|+10<55

9|x+8|<45|x+8|<5

-5<x+8<5

x-13 and x<-3

-13<x<-3

500

evaluate (|3x+2|)/(|x-1|)>2

x<-(2/3), -(2/3)<=x<1, x>=1

x<-4 or 0<x<1 or x>1

Inverse Functions

100

f(x) = x +56

y=x+56

x=y+56

SOLUTION - x-56=y

200

f(x) = 2x+14

y=2x+14

x=2y+14

x-14=2y

SOLUTION - (x-14)/2=y

300

f(x) = 8x²+64

y=8x²+64

x=8y²+64

SOLUTION - sqrt(2)sqrt(x-64)//4 - sqrt(2)sqrt(x-64)//4

400

f(x) = 576x²+81

y = 576x²+81

x = 576y²+81

SOLUTION - sqrt(x-81)//24, - (sqrt(x-81)//24)

500

f(x) = 4|6-2a|+8<=24

4(|-2a+6|)+8<=24

4(|2a+6|)<16

|-2a+6|<=4

-2a+6<=4 and -2a+6>=-4

SOLUTION - a>=1 and a<=5