Quadratics Gauntlet (400 & 500 isn't fun :))

Multiplying Polynomials by Monomials

100

12x²(2x + 17)

24x³ + 204x

200

-x⁴(a + b + x⁵)

-ax⁴ - bx⁴ - x⁹

300

ax(a³ - ax + a - x^-2)

Write with positive exponents!

a⁴x - a²x² + a²x - a/x

400

rx⁴y^-2(-r + xy⁴ - y^-1 + r^-1x^-4y²)

Write with positive exponents!

-r²x⁴1/y + rx⁵y² - rx⁴1/y³ + 1

500

(a^-2b^-3c^-7)(a + 7x - a²bc)

Write using positive exponents

1/(ab³c⁷) + 7x/(a²b³c⁷) - 1/(b²c⁶)

Multiplying Binomials

100

(x + 4)(x - 2)

x² + 2x - 8

200

(-x + 3)(x + 12)

-x² - 9x + 36

300

(-3x - 14)(3x - 14)

-9x² - 84x + 196

400

(-x - (-9))(x - (-17x))

-x² - 8x + 153

500

-(9x - 13)(9x - 13)

-81x² + 234x - 169

Multiplying Polynomials

100

(x + 2 + 3y)(x + 9)

x² + 11x + 3xy + 27y + 18

200

(x² - 3x -9)(2 - x)

-x³ + 5x² + 3x - 18

300

(-x² + 17x - 12)(x³ - 13)

-x⁵ + 17x⁴ - 12x³ +13x² -221x + 156

400

-(8x + 7)(-x⁴ - 12x + 14x³ - 2)

8x⁵ - 105x⁴ - 98x³ +96x² + 100x + 14

500

(-x⁴ - 12x + (-18))(x^-3 - 14x² + 12x - 2)

14x⁶-12x⁵+2x⁴+168x³-119x²-193x+36-12x^-2-18x^-3

Dividing Polynomials

100

(x³ + 2x² - 7x -12) / (x + 3)

x² - x - 4

200

(x³ + 5x² + 10x + 6) / (x + 1)

x² + 4x + 6

300

(x⁴ +16x³ + 67x² + 63x - 70) / (x + 10)

x³ + 6x² + 7x - 7

400

(x⁴ - 5x³ + 10x² - 3x -2) / (x - 1)

x³ - 4x² +6x + 3 + 1/(x-1)

500

(x⁴ - 9x³ + 24x² - 20x + 11) / (x -4)

x³ - 5x² + 4x - 4 - 5/(x - 4)

Factoring Polynomials

100

x² + 1x - 6

(x - 2)(x + 3)

200

2x² + 11x + 15

(2x + 5)(x + 3)

300

x² + 23x + 130

(x - 10)(x - 13)

400

4x² - 324

4(x - 9)(x + 9)

500

21x² - 80x - 84

(-7x - 6)(-3x + 14)