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. Factor the polynomial 6x² - 7x - 20 a) (2x - 5)(3x + 4) b) (3x - 5)(2x + 4) c) (2x + 5)(3x - 4) d) (3x + 5)(2x - 4) To factor the polynomial, find two binomials whose product gives the original polynomial: 6x² - 7x - 20 First, find two numbers that multiply to give the product of the leading coefficient (6) and the constant (-20), which is -120. The two numbers that multiply to give -120 and add to give the middle term coefficient (-7) are -15 and 8. Now, rewrite the polynomial, replacing the middle term with the sum -15x + 8x: 6x² - 15x + 8x - 20 Factor by grouping: 3x(2x - 5) + 4(2x - 5) Both expressions in parentheses are the same, so factor it out: (2x - 5)(3x + 4) 2 / 5 2. If f(x) = 2x² + 3x - 5 and g(x) = x + 1, find f(g(x)). a) 2x³ + 7x² + 5x - 6 b) 2x³ + 5x² - x - 7 c) 2x² + 5x - 6 d) 2x³ + 6x² + 5x - 1 To find f(g(x)), substitute g(x) into the f(x) equation. f(x) = 2x² + 3x - 5 g(x) = x + 1 f(g(x)) = 2(g(x))² + 3(g(x)) - 5 Substitute g(x) = x + 1: f(g(x)) = 2(x + 1)² + 3(x + 1) - 5 Expand the equation: f(g(x)) = 2(x² + 2x + 1) + 3x + 3 - 5 Simplify: f(g(x)) = 2x³ + 7x² + 5x - 6 3 / 5 3. Simplify the expression: (2x³ - x)/(x) a) 2x² - 1 b) 1x² - 1 c) 2x² - x d) 1x² - x To simplify the expression, divide each term in the numerator by the denominator: (2x³ - x)/(x) Divide the x³ term and the x term by x: 2x² - 1 Simplify: 2x² - 1 4 / 5 4. Simplify the expression: 5x - 2x² + 3x² - 7x + 2 a) x² - 2x + 2 b) x² - 2x - 2 c) x² + 2x + 2 d) x² + 2x - 2 To simplify the expression, combine the like terms. 5x - 2x² + 3x² - 7x + 2 Combine the x² terms and the x terms: (-2x² + 3x²) + (5x - 7x) + 2 Simplify: x² - 2x + 2 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