U8 Polynomials & Factoring

Adding/Classifying Polynomials

100

Add the Polynomials

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

5x + 5

Linear Binomial

200

Add the polynomials:

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

4a + 3

Linear Binomial

300

Add the polynomials:

(x² +3x + 5) + ( -x² +6x)

9x + 5

Linear Binomial

400

Add the polynomials:

(t² + 3t³ -3) + (2t² +7t -2t³)

t³ +3t² +7t -3

Cubic Polynomial

500

Add the polynomials:

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

Quadratic Monomial

Subtracting/Classifying Polynomials

100

Subtract the polynomials:

(g - 4) - (3g - 6)

-2g + 2

Linear Binomial

200

Subtract the polynomials:

(-5h - 2) - (7h +6)

-12h - 8

Linear Binomial

300

Subtract the polynomials:

(-x² - 5) - (-3x² -x -8)

2x² + x +3

Quadratic Trinomial

400

Subtract the Polynomials:

(k² + 6k³ -4) - (5k³ + 7k -3k²)

k³ + 4k² -7k -4

Cubic Polynomial

500

Subtract the Polynomials:

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

Quadratic Trinomial

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴)

6x⁶

200

Multiply the Polynomials:

(x - 3)(x + 2)

x² - x - 6

300

Multiply the Polynomials:

(2m - 1)(m + 2)

2m² + 3m - 2

400

Multiply the Polynomials:

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

12n² + 13n - 4

500

Multiply the Polynomials:

(d + 3)(d² - 4d + 1)

d³ - d² -11d + 3

Factoring GCF/ Special Products

100

Factor:

x⁴-42x²

x²(x²-42)

200

Factor:

5a³+10a²

5a²(a+2)

300

Factor:

2x² - 8

2(x+2)(x-2)

400

Factor:

4p² - 361

(2p+19)(2p-19)

500

Factor:

x²+46x+529

(x+23)²

Factoring

100

Factor:

p² +2p -35

(p-5)(p+7)

200

Factor:

z² - 4z - 21

(z+3)(z-7)

300

Factor:

-5y² - 22y - 8

-(5y+2)(y+4)

400

Factor:

x² - 3x + 4ax - 12a

(x+4a)(x-3)

500

Factor:

n³ - 9n

n(n+3)(n-3)

Word Problems

100

Find the area of a rectangle if the length is (x-5) and the width is (x+9).

x²+4x-45

200

Find the area of a trapezoid if b₁=2x+1, b₂=4x-5, and h=2x+5

A=1/2(b₁+b₂)h

6x²+11x-10

300

The area of a rectangular pool is 5x²+58x+80. If the length is (x+10), what is the width?

(5x+8)

400

The volume of a rectangular prism is x³+x²-4x-4. What are the dimensions of the object?

(x+2), (x+1), (x-2)

500

A rectangular garden has a width of 4 ft and a length of 6 ft. There is a border around the garden that is x ft by x ft. What is the area of the garden and the border?

4x²+20x+24 ft²