Polynomials

Add

100

(-4x+9) + (6x-14)

2x-5

200

(-3x-2) + (7x+5)

4x+3

300

(x²+3x+5) + (-x²+6x-4)

9x+1

400

(x²+3x³-3)+(2x²+7x-2x³)

x³+3x²+7x-3

500

(8x²-7x+4) +(9x-12x²)

-4x²+2x+4

Subtract

100

(g-4) - (3g-6)

-2g+2

200

(-5h-2) - (7h+6)

-12h-8

300

(3a²+a-9) - (4a²-3a+8)

-a²+4a-17

400

(-x²-5) - (-3x²-x-8)

2x²+x+3

500

(k²+6k³-4) - (5k³+7k-3k²)

k³+4k²-7k-4

Multiply

100

5c(3c⁵)

15c⁶

200

(4x-2)(4x+2)

16x²-4

300

(a-1)(2a+5)

2a²+3a-5

400

(x-2)(x²+x-1)

x³-x²-3x+1

500

(3n²+2n-5)(2n+1)

6n³+7n²-8n-5

Divide

100

(n⁴-2n²+6n) / n

n³-2n+6

200

(16k⁴-12k³+7k²) / k²

16k²-12k+7

300

(3k⁵-9k⁶-12k³) / 3k²

-3k⁴+k³-4k

400

((3b-9)(b+2)) / (b-3)

3(b+2)   or   3b+6

500

((3n-4)(4n+4)) / (n+1)

4(3n-4)      or     12n-16

Solve

100

x(x+5) = 0

x=0 and x=-5

200

(x-3)² = 0

x=3

300

Factor:  6x²+3x

3x(2x+1)

400

6x²=-72x

6x²+72x=0

6x(x+12) =0 

6x=0       x+12 = 0

x=0        x=-12

500

You build a weird fireplace.  The height in feet of the arch above the ground is modeled by the equation y=-0.1x²+1.4x, where x is where the arch hits the ground.  How wide is the fireplace?

0=-0.1x²+1.4x

0=x(-0.1x+1.4)

0=x         0=-0.1x+1.4.            Width = 14 ft

               -1.4 = -0.1x

               14 = x