Polynomial Games!

Peak Points

100

 f(x)=x³+4x²-5x-2b.

Minimum:(-4-√31/3, 308-62√31/27)

Maximum:(-4+√31/3, 308+62√31/27)

Domain:(-∞,∞)

Range:(-∞,∞)

X-intercepts:(1,0)(-5,0)

200

h(x)=x⁴-3x³+x²+4x-3

Maximum:(-0.3,-3)

Minimum:(-1,-9)

Domain:(-∞,∞)

Range:(-3.21,∞)

X-Intercepts:(-1.2,0) (1,0)

300

k(x)=3x³-2x²+5x-1

Maximum:no maximum

Minimum:(-5/2, -29/4)

Domain:(-∞,∞)

Range:(-∞,∞)

X-Intercepts:(0.2,0)

400

m(x)=4x⁴-7x³+3x²+3x-2

Maximum:(2,4)

Minimum:(-0.2, -2.4)

Domain:(-∞,∞)

Range:(-2.4,∞)

X-Intercepts:(-0.7,0)(0.7,0)

500

n(x)=x³-5x²+8x-2

Maximum:(0,4)

Minimum:(3,4)

Domain:All real numbers

Range:(-∞,∞)

X-Intercept:(0,0) (3,0)

Factor Frenzy

100

-3x³+5x²-2x+8

(x²+2)

(-3x+5)

200

 x²-8x+16 

(x-4)²

Or (x-4)(x-4)

300

 x³-27

(x-3)(x²+3x+9)

400

 x³-125

(x-5)(x²+5x+25)

500

3x³-27x

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

Dividing Decipher

100

Divide 3x³-4x²+2x-5 by x+2 using long division.

3x²-10x+22-49/x+2

200

divide 4x⁵-6x³+2x²-3x+1 by x-1 using long division

4x⁴+4x³-2x²-3-2/x-1

300

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

3x⁴-2x³+2x²-4x+4-6/x+1

400

Divide 3x³-2x²+5x-4 by x+3 using synthetic division

3x²-11x+38-118/x+3

500

Divide 4x⁴-2x³+5x²+x+3 by x-2 using long division

4x³+6x²+17x+35+73/x-2

Expert Strategies

100

4x²-25

(2x-5)(2x+5)

200

Factor 2x³-12

2(x³-6)

300

x²-9=0

x=+-3

400

8x³-125=0

x=5/2

500

x⁴-16=0

x=+-2

Bonus questions

100

x³+64

(x+4)(x²-4x+16)

200

4x³+2x²-6x+12=0

x=-2 or no real solution

300

x²-6x+9=0

x=3

400

Factor x³-264

(x-6)(x²+6x+36)

500

x⁴-8x²+16=0

x=+-2