Geometry Final

Prime Factorization & GCF

100

Factor the following polynomial using the GCF: 10x²y³-15x³y²

5x²y²(2y-3x)

200

Find the prime factorization of the following number: 40.

2³ * 5

300

Factor the following polynomial using the GCF: 2xy²z³+2x²y³z-8x³yz²

2xyz(yz²+xy²-4x²z)

400

Find the prime factorization of the following number: 972. 

2² * 3⁵

500

Factor the following polynomial using the GCF: x⁵+6x³y²-13x²y⁴+27x³y³

x²(x³+6xy²-13y⁴+27xy³)

Polynomials

100

Given f(x)=9x+13 and g(x)=2x-4, find f(x)+g(x).

11x+9

200

Given f(x)=2x²+9x-14 and g(x)=16x²+3, find f(x)+g(x).

18x²+9x-11

300

Given f(x)=12x-8 and g(x)=3x+6, find f(x)-g(x).

9x-14

400

Given f(x)=-2x²-x-20 and g(x)=2x²+4x+6, find f(x)-g(x).

-4x²-5x-26

500

Given f(x)=12x-7, g(x)=3x²+9x-11 and h(x)=7x²+14, find f(x)+g(x)-h(x).

-4x²+21x-32

Multiplying Binomials

100

Multiply the following binomials: (x+5)(x-4)

x²+x-20

200

Multiply the following binomials: (3x-8)(x+2)

3x²-2x-16

300

Multiply the following binomials: (4x+3)(7x+9)

28x²+57x+27

400

Multiply the following binomials: (29x+4)(14x-3)

406x²-31x-12

500

Multiply the following binomials: (12x²-19)(13x²+6)

156x⁴-175x²-114

Exponents & Radicals

100

Simplify the expression: 3x²y⁴(2x^-6y³)

(6y^7)/x^4

200

Simplify the radical: 

sqrt(92x^4y^7)

2x^2y^3sqrt(23y)

300

Simply the expression:

(2x^3y^4(6x^7y^8)^0)/(13x^7y^2)

(2y^2)/(13x^4)

400

Simplify the radical: 

sqrt(432x^13y^27z^16)

12x^6y^13z^8sqrt(3xy)

500

Simplify the expression: 

(5x^7y^3(2x^2y)^-3)/(2x^3y^6)

5/(16x^2y^6)

Factoring & Quadratic Formula

100

Factoring the following polynomial: x²+3x+2

(x+2)(x+1)

200

Solve using the quadratic formula: x²-8x+15=0

x=3 x=5

300

Factoring the following polynomial: 7x²+53x+28

(7x+4)(x+7)

400

Solve using the quadratic formula: 4x²-15x-23=2

x=5 x=-1.25

500

Factoring the following polynomial: 15x²-27x-6

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