Algebra 2

Synthetic Division

100

The dividend in (6x³-7x²+2)/(3x+1)

What is (6x³-7x²+2)?

200

The solution of (-2x²-5x+1)/(x-4)

What is (-2x -13 -⁵¹/_x-4)?

300

The solution of (3x³-2x²-150)/(x-4)

What is (3x²+10x+40+ ¹⁰/_x-4)?

400

The solution of (8x⁴-4x²+x+4)/(2x+1)

What is (4x³-2x²-x+1+³/_2x+1)?

500

The solution of (6x⁴-3x³-18x²-36x-9)/(3x+1)

What is [-2x³+(x²/3)+(55x/9)+(379/27)+(622/27{3x-1})]?

Binomial Theorem

100

The solution of (x+y)⁰

What is 1?

200

The solution to (x+y)³

What is x³+3x²y+3xy²+y³

300

The number of terms in (x+y)⁵

What is 6 terms?

400

The 7th row of the Pascal looks like

What is 1, 7, 21, 35, 35, 21, 7, 1?

500

The solution of (x+y)¹⁰ 

What is x¹⁰+ 10x⁹y+ 45x⁸y² +120x⁷y³ + 210x⁴y⁶ +120x³y⁷+ 45x²y⁸ +10xy⁹ + y^{10 ?}

Combination and Permutation

100

A combination is 

What is the mathematical technique that determines the number of possible arrangements in collection of items where the order of selections does not matter

(Anything similar counts)

200

The solution of ⁶C₃

What is 20?

^6!/_3!(6-3)!=20

300

The solution of ⁶P₃​​​​

What is 120?

^6!/_6-3!= 120

400

The formula for combination

The formula for permutation

(in terms of x and y)

What is ^xC_y= ^x!/_y!(x-y)!

What is ^xP_y= ^x!/_(x-y)!

500

The difference of ¹⁰P₅ and ¹⁰C₅

What is 29988

30,240(¹⁰P₅)- 252(¹⁰C₅)= 29988

Factoring by Grouping

100

The solution of 7y²-14y+9y-18

What is (7y+9)(y-2)?

200

The solution of 4x³-12x²+7x-21

What is (x-3)(4x²+7)?

300

The solution of 3x²-10x-8

What is (3x+2)(x-4)?

400

The solution of 5x²+16x+3

What is (5x+1)(x+3)?

500

The solution of 9x²+4x-5

What is (9x-5)(x+1)?

Polynomial Long Division

100

The solution of (2x²-9x-35)/(x+7)

What is 2x-23+¹²⁶/_x+7 ?

200

The solution of (x²-19x-11)/(x+8)

What is ^x-27+181/_x+8?

300

The solution of (-x³+16x²-13x+5)/(x+4)

What is -x²+20x-93+³⁷⁷/_x+4?

400

The solution of (2x³+13x²-14x+4)(x+3)

What is -x²+20x-93+¹⁰⁹/_x+3?

500

The solution of (20y³+23y²-13y+9)/(5y²-3y+2)

What is 4y+7-⁵/_(5y²-3y+2)?