Polynomial Games!

Maximums and Minimums!

100

f(x)=x³−2x²−3x+1

Minimum point: (-1,-6)

Maximum point: (3,4)

Domain: All real numbers

Range:(-∞,∞)

X-intercepts:(-1,0) and (3,0)

200

g(x)=x⁴−4x³+2x²+5x−2

Minimum point: (-1,-6)

Maximum point: (2,3)

Domain: All real numbers

Range:(-∞,∞)

X-intercepts:(-1,0) and (2,0)

300

h(x)=2x³+3x²-6x-4

Minimum point: (-2,-10)

Maximum point: (1,1)

Domain: All real numbers

Range:(-∞,∞)

X-intercepts:(-2,0) and (1,0)

400

k(x)=3x⁴-8x³+4x²+2x+1

Minimum point: (-1,-4)

Maximum point: (2,5)

Domain: All real numbers

Range:(-∞,∞)

X-intercepts:(-1,0) and (2,0)

500

m(x)=x³-6x²+9x+4

Minimum point: (0,4)

Maximum point: (3,4)

Domain: All real numbers

Range:(-∞,∞)

X-intercepts:(0,0) and (3,0)

Factoring Fun!

100

2x³-3x²+4x-6

x²(2x-3)+2(2x-3)

(2x-3)(x²+2)

200

x²-9

(x-3)(x+3)

300

x³+8

(x+2)(x²-2x+4)

400

x³-27

(x-3)(x²+3x+9)

500

4x³-16x

4x(x²-4)

Division Delights!

100

Divide 2x³+5x²−3x+1 by x+2 using long division.

2x²-x+1 and the remainder is 11

200

divide 3x⁴-7x²+4x-2 by x-1 using long division

x³+x²+3x+2

300

Divide 4x⁵+2x⁴-5x²+3 by x+1 using synthetic division

4x⁴-2x³+2x²-3x+1 and the remainder is 6

400

Divide 2x³-4x²+7x-3 by x+3 using synthetic division

2x²-10x+1 

500

Divide 5x⁴+3x³-6x²+2 by x-2 using long division

x³+5x²+14x+30 and the remainder is 82

Advanced Techniques

100

9x²-16

(3x-4)(3x+4)

200

8x³-27

(2x-3) (4x²+6x+9)

300

x²+4=0

x=+-2i 

400

27x³-64

(3x-4)(9x²+12x+16)

500

x⁴+4=0

x=+-√2i

Final challenges

100

x³-8

(x-2)(x²+2x+4)

200

2x³+6x²+4x+8

(x+1)(x²+2)

300

x²+4x+4=0

x=-2i

400

x³+27

(x+3)(x²-3x+9)

500

x⁴+4x²+4=0

x=+-2i