Exponent Rules & Polynomials

Product Rule

100

x^3 * x^6

x^9

200

2x^5 * x^7

2x^12

300

(4f^8)(6f^4)

24f^12

400

(8r^5)(2r^-7)

16/r^2

500

(7s^5p^3)(3s^6p^-5)

(21s^11)/p^2

Power Rule

100

(x^4)^5

x^20

200

4(y^3)^2

4y^6

300

(xy)^6

x^6y^6

400

(4w^5)^2

16w^10

500

(8w^3y^7)^0

1

Quotient Rule

100

x^7/x^3

x^4

200

(2x^6)/(x^5)

2x

300

(8x^10)/(4x^3)

2x^7

400

u^2/u^9

1/(u^7)

500

(4m^4)/(8m^8)

1/(2m^4)

Adding and Subtracting Polynomials

100

(x²+2)+(5x²-6)

6x²-4

200

(3x³-6x²)-(5x³+4x²)

-2x³-10x²

300

(9x³+5x²+11x)+(-2x³-8x²+9x)

7x³-3x²+20x

400

(3x⁴+8x³-6)-(x⁴-7x³-3)

2x⁴+15x³-3

500

(4x²+7x³)-(-6x²-7x³-4x)-(10x+9x²)

14x³+x²-6x

Naming Polynomials

100

x²-2

Quadratic Binomial

200

3x

Linear Monomial

300

2

Constant Monomial

400

7x³-2x-9

Cubic Trinomial

500

x⁴-x³+x²+10x-8

Quartic Polynomial

Multiplying Polynomials

100

x(x²+4x-12)

 x³+4x²-12x

200

2x²(4x³-2x-10)

8x⁵-4x³-20x²

300

(x-4)(x+8)

x²+4x-32

400

(2x+3)(4x-5)

8x²+2x-15

500

(x+2)(x²+5x-1)

x³+7x²+9x-2