12345 - 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: (3x² - 3x + 1) + (2x² + x + 4) a) 5x² - 2x + 5 b) 5x² - 2x + 5 c) 3x² - 2x + 5 d) 5x² - 2x - 5 To add the polynomials, combine the like terms. (3x² - 3x + 1) + (2x² + x + 4) 3x² + 2x² - 3x + x + 1 + 4 Combine the like terms: 5x² - 2x + 5 2 / 5 2. 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) 3 / 5 3. Find the product: (3x - 2)(x + 4) a) 3x² + 10x - 8 b) 3x² - 10x + 8 c) 3x² - 10x - 8 d) 3x² + 2x - 8 To find the product, use the distributive property (FOIL): (3x - 2)(x + 4) Multiply the first terms, outer terms, inner terms, and last terms: 3x(x) + 3x(4) - 2(x) - 2(4) Simplify the expression: 3x² + 12x - 2x - 8 Combine the like terms: 3x² + 10x - 8 4 / 5 4. Simplify the rational expression: (x² - 4x + 4)/(x² - x) a) (x - 2)²/[x(x + 1)] b) (x - 2)²/[x(x - 1)] c) (x - 2)²/[x(x + 2)] d) (x + 2)²/[x(x + 1)] First, factor the numerator and denominator: (x² - 4x + 4)/(x² - x) Factor the numerator as a perfect square: (x - 2)²/(x² - x) Factor x from the denominator: (x - 2)²/x(x - 1) We cannot simplify the expression further. So the simplified expression is: (x - 2)²/[x(x - 1)] 5 / 5 5. Multiply the polynomials: (x - 4)(x + 3) a) x² - x - 12 b) x² + x - 12 c) x² - x + 12 d) x² + x + 12 To multiply the polynomials, use the distributive property (FOIL): (x - 4)(x + 3) Multiply the first terms, outer terms, inner terms, and last terms: x(x) + x(3) - 4(x) - 4(3) Simplify: x² + 3x - 4x - 12 Combine the like terms: x² - x - 12 Your score is 0% Restart Quiz