Operations with Polynomials

Determining/Degree/Leading Coefficient/Standard Form

100

Degree of 5x⁴ + 2x³ - 3x² + 6x - 7

4

200

Degree of xy - 3x²y³ - 4xy³ + 7x⁵y?

6

300

Leading Coefficient of xy - 3x²y³ - 4xy³ + 7x⁵y?

7

400

Standard Form of xy - 3x²y³ - 4xy³ + 7x⁵y?

7x⁵y - 3x²y³ - 4xy³ + xy

500

Is this a polynomial 4xy^-3 + 2xy - 5x²y² + 7x⁵y⁸ AND is it quadratic?

NO

Adding & Subtracting

100

The sum of (5x-9) and (-2x -10)

3x - 19

200

(x² - 4x + 11) - (8x² - 7x + 2)

-7x² + 3x + 9

300

2(-4x + 15) - 3x(6x + 1)

-18x² - 11x + 30

400

Subtact 2a - 9b from -7a + 12b

-9a + 21b

500

The difference when 6x² - 5x + 2 is subtracted from -7x² + 9

-13x²+ 5x + 7

Multiplying

100

(5a⁵b⁴) (-6ab)

-30a⁶b⁵

200

17x - 2(3x - 8)

11x + 16

300

4yz (5y²+ 12z³)

20y³z + 48yz⁴

400

(3x + 5)²

9x² + 30x + 25

500

(x - 9)(x² - 8x -6)

x³ - 17x² + 66x + 54

Laws of Exponents

100

4x² * 4x³

16x⁵

200

(2x⁴y²)³

8x¹²y⁶

300

49x³y⁸z / 7xyz

7x²y⁷

400

(6a⁴b³)² / 4a³b⁵

9a⁵b

500

[(3x²y³)² * (2xy²)³] / (2xy)²

18x⁵y¹⁰

Dividing

100

Can you use synthetic division for (3n³ - 28n² + 18n - 4) / (3n - 1) ??

NO

200

Can you use synthetic division for (x⁴ - 10x³ - 5x + 45) / (x - 10)

Why??

YES, because you are dividing by 1x +/- # (x - 10)

300

(x⁴ - 10x³ - 5x + 45) / (x - 10)

x³ - 5 + (-5/x-10)

400

(3n³ - 28n² + 18n - 4) / (3n - 1)

n² - 9n + 3 + (-1/3n-1)

500

(-17 - 71x² - x³ - 83x + 9x⁴) / (9x + 8)

x³ - x² - 7x - 3 + (7/9x+8)