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: 2x² - 8x a) 2x(x - 4) b) 2x(x + 4) c) x(x - 4) d) 2(x - 4) To factor the polynomial, first find the greatest common factor (GCF) of the terms: 2x² - 8x The GCF of 2x² and 8x is 2x. Now, factor the GCF from the polynomial: 2x(x - 4) 2 / 5 2. Factor the polynomial: x² - 5x + 6 a) (x - 3)(x - 2) b) (x + 3)(x + 2) c) (x - 3)(x + 2) d) (x + 3)(x - 2) To factor the polynomial, find two binomials whose product gives the original polynomial: x² - 5x + 6 Find two numbers that multiply to give the product of the leading coefficient (1) and the constant (6), which is 6. The two numbers that multiply to give 6 and add to give the middle term coefficient (-5) are -3 and -2. Now, factor the polynomial: x² - 5x + 6 = (x - 3)(x - 2) 3 / 5 3. 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 4 / 5 4. Multiply the polynomials: (x + 3)(x - 2) a) x² + x - 6 b) x² - x - 6 c) x² + 5x - 6 d) x² - x + 6 To find the product, use the distributive property (FOIL): (x + 3)(x - 2) Multiply the first terms, outer terms, inner terms, and last terms: x(x) + x(-2) + 3(x) + 3(-2) Simplify the expression: x² - 2x + 3x - 6 Combine the like terms: x² + x - 6 5 / 5 5. Simplify the expression: (-3x² + 5x - 2) - (2x² - 3x + 1) a) -5x² + 2x - 3 b) -5x² - 8x + 3 c) -3x² + 8x + 3 d) -5x² + 8x - 3 To subtract the polynomials, distribute the negative sign and combine like terms. (-3x² + 5x - 2) - (2x² - 3x + 1) -3x² + 5x - 2 - 2x² + 3x - 1 Combine the like terms: -5x² + 8x - 3 Your score is 0% Restart Quiz