The Advanced Algebra Jeopardy

Pascal's triangle

100

What is the expansion of (a+b)³?

a³+3a²b+3ab²+b³

200

What is the expansion for (a+3b)⁴?  

a⁴+12a³b+54a²b²+104ab³+81b⁴

300

What is the expansion for (3x-2)⁵

243x⁵-810x⁴+1080x³-720x²+240x-32

400

The expansion of (2x-y)⁷

128x⁷-448x⁶y+672x⁵y² -560x⁴y³+280x³y⁴ -84x²y⁵+14xy⁶   -y⁷

500

The expansion of (x+2)¹⁰

x¹⁰+20x⁹+180x⁸+960x⁷+3360x⁶+8064x⁵+13440x⁴+15360x³+11520x²+5120x+1024

Long division

100

The quotient of (2x²+7x+11)/(x+2)

2x+3 R=5

200

The quotient of (9x³-15x²+4x) / (x-3)

9x²+12x  R=-32x

300

The quotient for (x³-x²-4x+4) / (x-2)

x²+x-2

400

The quotient for (x³+5x²+11x+15) / (x+3)

x²+2x+5

500

The quotient for (4x³+21x²-x-24) / (x+5)

4x²+x-6 R=6

Finding inverses

100

The inverse of y=(x-8)² (sqrt=square root)

y=sqrt(x)+8

200

The inverse of y=(3x-4)²

y=1/3sqrt(x)-4/3

300

The inverse for y=(3-2x)²-1

y=-1/2sqrt(x+1)-3/2

400

The inverse of f(x)=sqrt(x+7)

f^-1(x)=x²-7

500

The inverse of f(x)=sqrt(-2x+3)

f^-1(x)=-1/2x²+3/2

Determining end behavior

100

End behavior of y=-x³-x²+3

Up & Down

200

End behavior for y=x⁴-7x²+3

Up & Up

300

End behavior for y=-7x³+8x²+x

Up & Down

400

End behavior for y=1-4x-6x³-15x⁶

Down & Up

500

End behavior for y=8x¹¹-2x⁹+3x⁶+4

Down & Up

Solving radical expressions

100

The solution to 3+sqrt(2x-3)=8

x=14

200

The solution for sqrt(2x+3)-7=0

x=23

300

The solution for sqrt(6-3x)-2=0

x=2/3

400

The solution for sqrt(4x-23)-3=2

x=12

500

The solution for sqrt(x+7)-x=1

x=2