Bartemio's Algebra Review

Adding & Subtracting Polynomials

100

Add the Polynomials

(4x + 9) + (x - 4)

5x + 5

200

Add the polynomials:

(-3a - 2) + (7a + 5)

4a + 3

300

Subtract the polynomials:

(-x² - 5) - (-3x² - x - 8)

2x² + x + 3

400

Add the polynomials:

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

500

Subtract (5k³ + 7k - 3k²) from (k² + 6k³ - 4)

k³ + 4k² - 7k - 4

Multiplying Polynomials

100

Multiply the Polynomials:

3x(2x - 5)

6x² - 15x

200

Multiply the Polynomials:

(x - 3)(x + 2)

x² - x - 6

300

Multiply the Polynomials:

(2m - 3)²

4m² - 12m + 9

400

Multiply the Polynomials:

(4n - 1)(3n + 4)

12n² + 13n - 4

500

Multiply the Polynomials:

(d + 3)(d² - 4d + 1)

d³ - d² - 11d + 3

Common Factors/ Special Products

100

Factor out the Greatest Common Factor (GCF):

5a³ + 2a²

a²(5a + 2)

200

Factor out the Greatest Common Factor (GCF):

30x² - 42x

6x(5x - 7)

300

Factor:

p² + 12p + 35

(p + 5)(p + 7)

400

Factor:

z² - 4z - 21

(z + 3)(z - 7)

500

Factor out the Greatest Common Factor (GCF):

18n⁴ + 42n² + 6n

6n(3n³ + 7n + 1)

Factor by Grouping

100

Factor by grouping: 

x³ - 2x² + x - 2

(x² + 1)(x - 2)

200

Factor by grouping: 

n³ - 8n² + 7n - 56

(n² + 7)(n - 8)

300

Factor by grouping: 

2x³ - 12x² - 7x + 42

(2x² - 7)(x - 6)

400

Factor by grouping: 

8m³ + 4m² - 6m - 3

(4m² - 3)(2m + 1)

500

Factor by grouping: 

12x³ - 9x² + 32x - 24

(3x² + 8)(4x - 3)

Graphing

100

What is the slope of the line containing these points (1,3) (-2,-6)?

What is m=3

200

Write and equation in slope intercept form that passes through (0,-6) and has a slope of -4

What is y=-4x -6

300

Change y+6 = 1/3 (x-9) to Standard Form

What is x-3y = 27

400

Write an equation in slope intercept form that passes through the points (5,0) and (4,5)

What is y=-5x + 25

500

Write the equation of a line that is Perpendicular to y=1/4x-2 and crosses through the point (-3, -3).

What is y = -4x -15 ?