Wilfrid Laurier University

• MA 100

• MA100 Lab Report 1 - Algebra Review Name: Student Number: Winter 2017 1. [6 marks] Solve the following equation for x. Where appropriate, state your answers in interval or set notation. (a)   √ 2
  x + 3   = 1 Either √ 2x + 3 = 1, or √ 2x + 3 = −1 : Case 1: √ 2x + 3 = 1 Case 2: √ 2x + 3 = −1 √ 2x = −2 √ 2x = −4 x = − √ 2 ≈ −1.414 x = − 4 √ 2 = − 2 2 √ 2 √ 2 √ 2 = −2 √ 2 ≈ −2.828 ∴ x = −1.414, or x = −2.828 (b)     x + 2 3     ≥ 7 Either x + 2 3 ≥ 7, or x + 2 3 ≤ −7 : Case 1: x + 2 3 ≥ 7 Case 2: x + 2 3 ≤ −7 x + 2 ≥ 21 x + 2 ≤ −21 x ≥ 19 x ≤ −23 Therefore, x ∈ (−∞, −23] ∪ [19, ∞) 2. [4 marks] Fully factor each of the following polynomials. (a) 9x 3 − 81x 9x(x 2 − 9) = 9x(x + 3)(x − 3) (b) x 2 − 14x + 48 Two factors that sum to -14 and multiply to 48 are -6 and -8. x 2 − 14x + 48 = (x − 6)(x − 8) (c) 6x 2 − 13x + 6 Two factors that sum to −13 and multiply to 36 are -9, -4. 6x 2 − 9x − 4x + 6 = 3x(2x − 3) − 2(2x − 3) = (3x − 2)(2x − 3) (d) x 4 + 4x 3 − 12x 2 x 4 + 4x 3 − 12x 2 = x 2 (x 2 + 4x − 12) two numbers that add to 4 and multiply to -12 are 6, -2. x 2 (x 2 + 4x − 12) = x 2 (x + 6)