Polynomials

Real Rational, Real Irrational, Imaginary

100

x = 1

Real Rational

200

x = 0, -1

Both Real Rational

300

x = ±4

Both Rational Rational

400

x = ± 3

x = ±√5

Real Rational, Real Irrational

500

x = 0

x = ±√3

x = 2i

Real Rational, Real Irrational, Imaginary

Finding Roots

100

-4x³ = 8x²

x = 0, -2

200

(x + 2)(x - 6) = x + 2

x = 7, -2

300

x² - 8x² + 7 = 0

x = ±√7, ±1

400

x³ + 2x² - 9x - 18 = 0 

x = -2, ±3

500

9x³ + 36x² - 4x - 16 = 0

x = -4, ±2/3

Degrees

100

2x⁶ - 32x² = 0

Degree: 6

200

x³ + 2x² - 3x - 6 = 0

Degree: 3

300

x⁴ + 2x³ = 8x²

Degree: 4

400

(x + 1)²(x - 6) = 0

Degree: 3

500

x³(x - 2)²(x² + 4x - 8) = 0

Degree: 7

Roots and Multiplicity

100

(4x - 1)(x + 3) = 0

x = 1/4, M1

x = -3, M1

200

(x + 1)²(x - 6) = 0

x = -1, M2

x = 6, M1

300

x⁴ + 2x³ = 8x²

x = 0, M2

x = -4, M1

x = 2, M1

400

x³ + 5x² + 7x + 35 = 0

x = -5, M1

x = i√ 7, M1

x = -i√ 7, M1

500

6x⁵ + 44x⁴ + 14x³ = 0

x = 0, M3

x = -1/3, M1

x = -7, M1

Lead Coefficient

100

3x³ - 6x + 7 = 0

Lead Coefficient: 3

200

-4x⁷ - 5 = 0

Lead Coefficient: -4

300

4x + 8x⁵ - 3x² + 4 = 0

Lead Coefficient: 8

400

-4x⁵ - x⁶ + 2x⁴ - 3x + 11 = 0

Lead Coefficient: -1

500

-x²(x + 7)(x - 4)³ = 0

Lead Coefficient: -1