UT Domain of The Expressions and Using the Laws of Exponents Question

Assignment 1Due October 4th – submission on Brightspace
Note: We haven’t covered everything in it yet, but we will before the deadline.
1. Compute the following expressions:
√
128
4
2
=
(a) −3 − (−3) − 5 · √4
64




(b) 3 (4 + 𝜋)2 − | − 𝜋2 | + 2−1 22 − 102 =
(c)
8
3
− 56

−
+
2
9
4
−3
=
−2
1
+
(d) −
−3
5
 −2
=
2. Write the sets in the simplest form and graph them.
(a) {𝑥 ∈ N | 𝑥 < 20} ∩ (−𝜋, 3𝜋] (b) (−∞, −𝜋) ∪ (−4, ∞) (c) (−5, 6] ∩ (3, 10) (d) [−7, 2] ∩ [2, 3] (e) Z ∩ (−3𝜋, 5) 3. Simplify using the laws of exponents and/or radicals: √ √ 4 3 3 𝑥 · 𝑥 𝑦4 = (a) √ 6 2√ 𝑦 𝑥 3√ 4 (9𝑎𝑏)− 2 𝑎 6 (b)  √  15 𝑏 −5 4. Write the polynomials in standard form: (a) (2𝑥 − 1)(3𝑥 + 5) (b) (−3𝑥 + 4)(𝑥 2 − 2𝑥 + 1) (c) −(𝑥 + 2)2 − 3(−𝑥 + 1)(2 − 𝑥 2 ) 5. What is the domain of the expressions below? (a) (b) (c) (d) √ 2−3𝑥 𝑥 𝑥 𝑥−3 3−𝑥 √ 𝑥+1 𝑥2 𝑥+2 𝑥 2 +3𝑥+2 6. Factor the polynomials below: (a) 𝑥 4 − 9𝑦 4 (b) −𝑥 3 + 27 (c) 100 + 𝑢 2 − 20𝑢 (d) 2𝑥 2 − 5𝑥 − 3 7. Solve the equations: (a) 4 = 3𝑥 − 5 (b) 6𝑥 2 + 11𝑥 + 3 = 0 (c) 𝑥 3 − 2𝑥 2 − 5𝑥 + 6 = 0 (d) 𝑦 4 − 13𝑦 2 + 36 = 0 8. Compute and simplify as much as possible the rational fractions: (a) (b) (c) 3𝑥 − 4 2 − 𝑥 − 𝑥+5 𝑥−3 2𝑥+3 2 − 𝑥 𝑥−1 −2 + 𝑥2 4 5−5𝑥 3𝑥 − 4 −𝑥 + 1 −2 2 + 4𝑥 + 3 2𝑥 + 𝑥 − 1