Algebra

Algebra Practice

1. Simplify the following

a. ( 1

2 )

−1 b. (

3

2 )

−2 c. (𝑥2𝑡 3)5 d. (4𝑦 2)−2

e.( 252

255 )

−3

f. (𝑥3𝑧 −2)−1 g. ( 5𝑥2

𝑎𝑏−1 )

−1

h. (𝑥−1𝑦 2)−3

2. Simplify the following

a. 1 − 1

1− 1

𝑥

b. 1 + 2−1

1+2−2

c. 𝑥−1 + 𝑦 −1 d. [1 − (1 + 𝑥−1)−1]−1

3.

4. Use the given zero to find the zeros of the function

a. g(x)=𝑥3 − 7𝑥2 − 𝑥 + 87 when 5+ 2i is a zero

b. ℎ(𝑥) = 3𝑥3 − 4𝑥2 + 8𝑥 + 8 when 1-√3𝑖 is a. zero

4. Find all the zeros of the function and write the polynomial as a product of linear factors. a. 𝑓(𝑥) = 𝑥3 − 2𝑥2 − 11𝑥 + 52

b. 𝑔(𝑥) = 𝑥4 − 4𝑥3 + 8𝑥2 − 16𝑥 + 16