Math Quiz -Polynomials Report a question What's wrong with this question? You cannot submit an empty report. Please add some details. Math Quiz -Polynomials Covering: performing operations with polynomials (addition, subtraction, multiplication, division, factoring), and simplifying and manipulating rational expressions, including the arithmetic of rational functions, as well as identifying and solving rational equations. 1 / 5 1. Add the polynomials: (2x² + 3x - 4) + (x² - x + 5) a) 3x² + 2x + 1 b) 2x² + 2x - 1 c) 3x² - x - 9 d) 2x² - x + 1 To add the polynomials, combine the like terms. (2x² + 3x - 4) + (x² - x + 5) 2x² + x² + 3x - x - 4 + 5 Combine the like terms: 3x² + 2x + 1 2 / 5 2. Factor the polynomial x² - 9 a) x² - 9 b) x - 3 c) x + 3 Note that the polynomial x² - 9 is in the difference of squares form: x² - 9 = (x - 3)(x + 3) 3 / 5 3. Factor the polynomial x³ - 8 a) (x - 2)(x² + 2x + 4) b) (x + 2)(x² - 2x + 4) c) (x - 2)(x² - 2x + 4) d) (x + 2)(x² + 2x + 4) To factor the polynomial x³ - 8, use the 'difference of cubes' formula: a³ - b³ = (a - b)(a² + ab + b²) where a = x and b = 2: x³ - 8 = (x - 2)(x² + 2x + 4) 4 / 5 4. Multiply the polynomial by a constant: -3(2x² - 5x + 4) a) -6x² + 15x - 12 b) -3x² + 15x - 12 c) 6x² + 15x - 12 d) 6x² - 15x + 12 To multiply the polynomial by a constant, multiply each term by the constant: -3(2x² - 5x + 4) Distribute the constant: -6x² + 15x - 12 5 / 5 5. Solve the equation: x² - 6x + 9 = 0 a) x = -3 b) x = 3, x = -3 c) x = 3 d) x = 0 To solve the equation, first factor the quadratic: x² - 6x + 9 = (x - 3)(x - 3) Set the factors equal to 0: (x - 3)(x - 3) = 0 x - 3 = 0 → x = 3 Since both factors are the same, there is only one solution: x = 3. Your score is 0% Restart Quiz