Chapter R - Review of Prerequisites

Exponents and Radicals

100

Simplify 

6y^0

6

200

Simplify 

(64/27)^(1/3)

4/3

300

Simplify 

(-3x)^-4(4x^-2y^3)^3

(64y^9)/(81x^10)

400

Simplify 

sqrt(15x)timessqrt(21x)

3xsqrt35

500

Simplify 

root3(625c^2d^10)/(root3(5c^5d)

(5d^3)/c

Polynomials and Factoring

100

Simplify 

(-4w^3-5w^2+6w+3)+(8w^2-4w+2)

-4w^3+3w^2+2w+5

200

Simplify 

(6.1a^2b+2.9ab-4.5b^2)-(2.6a^2b-4.1ab+2.1b^2)

3.5a^2b+7ab-6.6b^2

300

Multiply 

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

6x-11sqrtx-35

400

Factor 

x^2-100

(x+10)(x-10)

500

Factor 

32x^4-162

2(4x^2+9)(2x+3)(2x-3)

Rational Expressions/Operations on Radicals

100

Determine restricted values 

x/(x^2-49)

x cannot be 7, -7

200

Simplify and list restrictions 

(x^2-16)/(x^2-x-12)

x cannot be -3, 4

(x+4)/(x+3)

300

Simplify 

7/(4a)+11/(10a^2)

(35a+22)/(20a^2)

400

Simplify 

(3x+5)/(x^2+4x+3)-(x-5)/(x^2+2x-3)

(2x)/((x+1)(x-1))

500

Simplify 

(x/4-4/x)/(1/4+1/x)

x-4

Equations with Real Solutions

100

Solve 

3(2x-1)=5x-4

x= -1

200

Solve 

3(2x-1)=2(3x-2)

no solution

300

Solve 

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

set of all real numbers

400

Identify Restrictions and Solve 

(2x)/(x-4)-(3)/(x+2)=(x^2+14)/(x^2-2x-8)

x cannot be 4, -2

x=1

500

Solve 

sqrt(x+10)-4=x

x= -1

x= -6 FAKE

Imaginary Numbers

100

Simplify 

sqrt (-25)

5i

200

Simplify 

sqrt (-12)

2isqrt 3

300

Simplify 

(-2-4i)+(5+2i)-(3-6i)

0+4i

400

Multiply 

(-2+6i)(4-3i)

10+30i

500

Simplify 

(8+2i)/(3-5i)

7/17+23/17i