Polynomials

Exponent Rules

100

Simplify (3x^6)/(2x^-4)

(3x^10)/2

200

Simplify (3x^6 y^5 z^3) / (6x^-2 y^5 z^0)

(x^8 z^3) / 2

300

Write (4.6 x 10^7) / (3.2 x 10^5) in scientific notation.

1.4375 x 10^2

400

Write (1.865 x 10^6)(3.28 x 10^3) in scientific notation.

6.1172 x 10^9

500

Simplify (2xy)^-3 / (xy)^4

1 / (8x^7 y^7)

Graphing

100

What is the degree of the polynomial f(x)=x^3 +3x^2 +9x -2x^7 +4

7

200

What is the type for the polynomial f(x)=3x^4 +3x^3 -2x +6

Quartic

300

What is the leading coefficient of the polynomial f(x)= -4x^6 +5x^2 -9x +8

-4

400

What are the zeros for the polynomial f(x)=4x^3 -6x +2?

-1.37, .37, and 1

500

What are the zeros for the polynomial function f(x)=4x^4 -2x^3+ 4x -6

-1.17 and 1

Operations

100

(-3x^6 + 5x^4 - 3x^3 -4x^2 +5x - 7) + (4x^6 +3x^3 - 5x^2 + 21x -1)

x^6 + 5x^4 - 9x^2 + 26x - 8

200

(x^9 - 7x^5 +3x^4 +2x -8) - (7x^9 +2x^5 - 3x^4 +7x -2)

-6x^9 - 9x^5 + 6x^4 - 5x - 6

300

(2x-4)^2

4x^2 - 16x + 16

400

x(x+1)(x-3)

x^3 - 2x^2 - 3x

500

(x^3 + 2x^2 - 5x - 6) / (x-2)

x^2 + 4x + 3

Factoring

100

Factor 81x^2 - 36

(9x+6) (9x-6)

200

3x^3 - 27x

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

300

x^3 + 4x^2 + 6x + 24

(x^2 +6)(x+4)

400

x^4 + 5x^2 +6

(x^2 +2)(x^2 +3)

500

Factor 64x^3 - 27

(4x-3)(16x^2 + 12x + 9)

Solving

100

6x^2 = 216

x= 6, x= -6

200

9x^2 + 3 = -42

x = sqrt (5)i , x= - sqrt(5)i

300

x^4 + 3x^2 - 18

x= +/- sqrt (6)i, x= +/- sqrt(3)

400

x^3 + 2x^2 - 4x - 8 =0

x= -2 and x=2

500

2x^3 - 18x

x=0, x=-3. x=3