Polynomials

Factoring Polynomials

100

Factor the following polynomial

(12x-4)

4(3x-1)

200

Factor the following polynomial

11x+13y

Prime

300

Factor the following polynomial

20bc²+28bc

4bc(5c+7)

400

Factor the following polynomial

35a²-20ab²+15a

5a(7a-4b²+3)

500

Factor the following polynomial

3a³b²c-9a²b³c²+15ab⁴c³

3ab²c(a²-3abc+5b²c²)

Standard Form/Classifying Polynomials

100

What two things must be true when writing a polynomial in standard form?

Alphabetical order and highest exponent first

200

Classify the following polynomial

3x³+1

Cubic Binomial

300

Write the following polynomial in standard form.

2 - 3x⁴ + x² + 10x³

- 3x⁴ + 10x³ + x² + 2

400

Classify the following polynomial

x⁴-2x³-600

Quartic Trinomial

500

Write the following polynomial in standard form.

2a²b³ - 3a⁴ + b² + 10ab³

- 3a⁴ + 2a²b³ + 10ab⁴ + b²

Adding/Subtracting Polynomials

100

(3x²-10) - (x²+3)

2x²-13

200

(x³+1) + (x³-1)

2x³

300

(9x²-4x+99) - (-3x²+8x+87)

12x²-12x+12

400

(10x⁵-9x) - (5x⁴+x+1)

10x⁵-5x⁴-10x-1

500

(3x⁴-2x³+x²-10x+13) + (-x⁴+x³+4x²+10x-13)

2x⁴-x³+5x²

Multiplying Polynomials

100

x^a * x^b

x^a+b

200

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

6x²+11x-10

300

(12x-1)²

144x²-24x+1

400

(2x-5)(4x²+x+3)

8x³-18x²+x-15

500

(6x³+9)(2x²-5x+11)

12x⁵-30x⁴+66x³+18x²-45x+99

Dividing Polynomials

100

x^a / x^b

x^a-b

200

42x¹⁰ / 3x

14x⁹

300

(40x²-8x) / 8

5x²-x

400

(6a²b-12ab²) / -2ab

-3a+6b

500

(40c⁵d⁹-12c⁴d⁸+4c³d⁷) / 4c²d²

10c³d⁷-3c²d⁶+cd⁵