Algebra 1...Polynomials and Factoring

Polynomials...name, add, subtract

100

Name the polynomial:  -6

Constant monomial

200

Name the polynomial:  3x²y + 2xy

cubic binomial

300

(2x² - 4x - 1) - (3x² + 8x - 4)=

-1x² - 12x + 3

400

(5b⁴ -2 + 3b²) + (5b² - 4 + 3b⁴) = 

8b⁴ + 8b² - 6

500

A garden center has (3x² + 12x +18) sq ft of sod. One week, they receive (4x² + 16x + 60) sq ft of sod, and sell (2x² + 9x + 27) sq ft of sod. What expression represents the area of the remaining sod?

5x² + 19x + 51

Multiplying Polynomials

100

Find the product:  

2x(x² + 6x + 13)

2x³ + 12x² + 26x

200

Find the product:

(x + 7)(x - 5)

x² + 2x - 35

300

Find the product:

(2x - 5)(3x + 1)

6x² - 13x - 5

400

Find the product:

(x + 4)(x² - 3x - 1)

x³ + x² - 13x - 4

500

The volume of a cube is calculated by multiplying the length, width, and height. If the side length is (3x - 1), what is the volume of the cube? 

27x³ - 27x² + 10x - 1

FOILing Special Cases

100

Multiply:  (b + 12)(b - 12)

b² - 144

200

Multiply:  (4x + 1)(4x + 1)

16x² + 8x + 1

300

Multiply:  (3x - 4y)(3x + 4y)

9x² - 16y²

400

Find the product:

(3a - 5b)²

9a² - 30ab + 25b²

500

Find the surface area of the cube if the side length of the cube is 5x - 2.

150x² - 120x + 24

Factoring Polynomials: GCF

100

Find GCF:

14x²y²; 84x³y⁵; 21xy³

7xy²

200

Use GCF to factor the polynomial:

15x³ - 42x

3x(5x² - 14)

300

Factor Using GCF:

6y⁵ - 42y³ + 18y

6y(y⁴ - 7y² + 3)

400

Factor using GCF:

49a⁵b³ - 14a²b² + 35ab

7ab(7a⁴b² - 2ab + 5)

500

Add the polynomials, then factor:

(8x² - 12x) + (6x² - 4x) =

14x² - 16x

2x(7x - 8)

Factor Trinomials

100

Factor:  x² + 12x + 35

(x + 5)(x + 7)

200

Factor:  x² + 7x - 18

(x + 9)(x - 2)

300

Factor:  x² - 14x +49

(x - 7)(x - 7)

400

Factor...Use GCF first:

12x² + 22x +6

2(3x + 1)(2x + 3)

500

Factor...Use GCF first:

3x² + 18x + 27

3(x + 3)(x + 3)