2023 Fall Semester Review

Operations With Polynomials

100

Simplify

(4-6m^4 +3m^3) + (2m^4 -7m+8)

-4m^4-4m^3+12

200

Simplify

(2a-5a^3+6a^4)-(3a^4+7a^3+2a)

3a^4-12a^3

300

Simplify

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

6x^3-9x^2+12x

400

Simplify

(2n-4)(3n+5)

6n^2-2n-20

500

Simplify (synthetic division)

(5b^2-9b-2) / ((b-1)

5b-4-6/(b-1)

Imaginary Numbers

100

Simplify

(2+i)(-8+i)

-17-6i

200

Simplify

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

-18-16i

300

Simplify

sqrt(-144)

12i

400

Simplify

sqrt(-225)

15i

500

sqrt(-108)

6isqrt(3)

Operations With Radicals

100

Simplify

-2sqrt6-3sqrt6

-5sqrt6

200

Simplify

-2sqrt18+2sqrt2

-4sqrt2

300

(sqrt4)/sqrt64

1/4

400

Simplify

sqrt10(sqrt5+sqrt2)

5sqrt2+2sqrt5

500

Simplify

sqrt3(-3sqrt6-4sqrt10)

-9sqrt2-4sqrt30

Finding Zeros

100

Solve

x^2+2x-48=0

6

-8

200

Solve

x^2+7x=0

-7

0

300

Solve

r^2+16r+64=0

-8

400

Solve

5x^2=-14x+24

6/5

-4

500

Solve

2x^2=-x

-1/2

0

Factoring

100

Factor

x^2+8x+15

(x+3)(x+5)

200

Factor

x^2-2x-15

(x-5)(x+3)

300

Factor

x^2-144

(x-12)(x+12)

400

Factor

9x^2-49

(3x-7)(3x+7)

500

Factor

7x^2-22x+16

(7x-8)(x-2)