6th bell Polynomial Review

Classifying Polynomials

100

Classify the following polynomial by degree and number of terms:

6x²+5x+8

Quadratic trinomial

200

Classify the following polynomial by degree and number of terms:

-2x²+4x³+x

Cubic trinomial

300

Classify the following polynomial by degree and number of terms:

x³+4x²+x⁵-2x+2

Quintic polynomial of 5

400

Classify the following polynomial by degree and number of terms:

x(x+2)(x-6)+12

Cubic polynomial of 4 terms

500

Classify the following polynomial by degree and number of terms:

(-8x³-7)+(-x³-6)

Cubic binomial

End Behavior

100

Determine the end behavior of the graph of each polynomial:

y=-x²

Down, Down

200

Determine the end behavior of the graph of each polynomial:

y=-7x³+8x²+x

Up, Down

300

Determine the end behavior of the graph of each polynomial:

y=x³-14x-4

Down, Up

400

Determine the end behavior of the graph of each polynomial:

y=-2x⁹+3x⁶+8x¹¹+4

Down, Up

500

Determine the end behavior of the graph of each polynomial:

y=x(5-17x⁷+9x⁹)

Up, Up

Relative Min and Max

100

Find the relative minimum and maximum of the function:

f(x)=x³+4x²-5x

The relative min is -1.378 at x=0.523

The relative max is 24.193 at x=-3.189

200

Find the relative minimum and maximum of the function:

f(x)=-x³+16x²-76x+96

The relative min is -16.901 at x=3.569

The relative max is 5.049 at x=7.097

300

Find the relative minimum and maximum of the function:

f(x)=-4x³+12x²+4x-12

The relative min is -12.317 at x=-0.155

The relative max is 12.317 at x=2.155

400

Find the relative minimum and maximum of the function:

f(x)=x³-7x²+7x+15

The relative min is -5.049 at x=4.097

The relative max is 16.901 at x=0.569

500

Find the relative minimum and maximum of the function:

f(x)=2x³-23x²+78x-72

The relative min is -7.138 at x=5.135

The relative max is 10.508 at x=2.532

Solve Sum or Difference of Cubes

100

Factor and solve the following equation:

x³-27=0

(x-3)(x²+6x+9)=0

200

Factor and solve the following equation:

x³+125=0

(x+5)(x²-5x+25)=0

300

Factor and solve the following equation:

x⁴+64x=0

x(x+4)(x²-4x+16)=0

400

Factor and solve the following equation:

6x³=48

6(x-2)(x²+2x+4)=0

500

Factor and solve the following equation:

8x³-1=0

(2x-1)(4x²+2x+1)=0

Solving Polynomials by Factoring

100

Factor and solve the following equation:

x⁴-10x²=-9

(x²-9)(x²-1)

x=3, -3, 1, -1

200

Factor and solve the following equation:

27=-x⁴-12x²

(x²+3)(x²+9)

x=3i, -3i, i(radical 3), -i(radical 3)

300

Factor and solve the following equation:

x⁴-12x²=64

(x²-16)(x²+4)

x=4, -4, 2i, -2i

400

Factor and solve the following equation:

x⁴-3x²=4

(x+2)(x-2)(x²+1)=0

x=1, -1, i, -i

500

Factor and solve the following equation:

x⁴+7x²=18

(x²+9)(x²-2)=0

x=-3i, 3i, (radical 2), -(radical 2)