Unit 2: Operations with Polynomials

Adding Polynomials

100

Solve (30x-8)+(15x+2).

What is 45x-6?

200

(2x²+51x-3)+(16x²-5x+3)

What is 18x²+46x?

300

(3x³+4x²+12x+3x⁴)+(8x⁴+10x³+8x²+14x)

What is 11x⁴+13x³+12x²+26x?

400

(15x¹⁶+17x⁴+3x+a⁵+5)+(3x⁴+40x¹⁶+7x-a⁵+1)

What is 55x¹⁶+20x⁴+10x+6?

500

(4x²-3x+9z³+3z)+(9x⁷+3z-128z³+421x+9)

What is 9x⁷+4x²+418x-119z³+6z+9?

Subtracting Polynomials

100

Solve (35x+14)-(21x-13).

What is 14x+27?

200

(7x²+72x+52)-(3x²-2x+40)

What is 4x²+74x+12?

300

(5x²+3x-6)-(3x²-x+5)

What is 2x²+4x-11?

400

(13b+15b²⁰-b-4)-(17b-6b²⁰+4b-16)

What is 21b²⁰-9b+12?

500

(700x²+609x+379)-(14003x²-41397x+378)

What is -13303x²+42006x+1?

Multiplying Polynomials

100

Complete the following: (x-8)(x+16).

What is x²+8x+8?

200

(x+8)(x+7)

What is x²+15x+56?

300

(5x²+x+7)(x-8)

What is 5x³-39x²-x-56?

400

2(15c³+3)(2c²+4)

What is 60c⁵+120c³+12c²+24?

500

(7x³+9x²-16x+9)(4x²-7)

What is 28x⁵+36x⁴-113x³-27x²+112x-63?

Dividing Polynomials

100

Solve: (x²+6x-27)÷(x-3).

What is x+9?

200

Solve (4x⁴+6x³+3x²+x+7)÷(x-2).

What is 4x³+14x²+31x+63+(133/x-2)?

300

(5x⁴+3x⁵+2x+3)÷(x-3)

What is 3x⁴+14x³+42x²+126x+380+(1,143/x-3)?

400

(3x⁴+12x²-x-5)(x-3)^-1

What is 3x³+9x²+39x+116+(343/x-3)?

500

(7x⁷-28x⁹+36x⁴-3000x²+7x+9)÷(x+2)

What is -28x⁸+56x⁷-105x⁶+210x⁵-420x⁴+876x³-1752x²+502x-997+(2003/x+2)?

Binomial Expansion

100

Solve (x-3)².

What is x²-6x+9?

200

(x+7y)²

What is x²+14xy+49y²?

300

(2+x²)³

What is x⁶+6x⁴+12x²+8?

400

(4x²-y³)⁴

What is 256x⁸-256x⁶y³+96x⁴y⁶+16x²y⁹+y¹²?

500

(4x²-5y³)⁶

What is 4,096x¹²-30,720x¹⁰y³+96,000x⁸y⁶-160,000x⁶y⁴+75,000x⁴y¹²-75,000x²y¹⁵+15,625y¹⁸?