CHAMPLAIN COLLEGE SAINT-LAMBERT Department of Mathematics Course: 201-103-GOLOVINA 2 Homework set Webwork 1 for Maxwell Gilletz Due: 01/24/2021 at 11:59pm EST INSTRUCTIONS: This is a WeBWorK homework set. Work out your assignment on paper, and enter the solutions into the computer. 1 2a 1. (1 point) 2 = Answer(s) submitted: 4. (1 point) (correct) 2. (1 point) 1 √ √ 11x 5 − 3y 3 then you will get A B where A = (x + y)2 = x2 + y2 . (x + y)2 = x2 + 2xy + y2 . x 1 x+y = y . x√− (x + y) = y. 2 √x = x. 2 √x = |x|. x2 + 4 = x + 2. 1 1 1 x+y = x + y . and B = Answer(s) submitted: • 11xsqrt5+3ysqrt3 • 605xˆ2-27yˆ2 (correct) 5. (1 point) F T F F F T F F 57 57 57 = + 82 + x 82 x 57 + a a 2. = 1+ 57 57 x + 57 x = 3. y + 57 y 82 82 = 1− 4. 82 − c c 1. (correct) 3. (1 point) Enter ”=” if the proposed identity holds, and ”N” otherwise. 1 2b 1 2 ab. 1 2a 1 2b ab 2 . 1 2a 1 2b ab 4 . Enter a T or an F in each answer space below to indicate whether the corresponding equation is true or false. An equation is true ony if it is true for all values of the variables. Disregard values that make denominators 0. You must get all of the answers correct to receive credit. Answer(s) submitted: If you rationalize the denominator of This problem addresses some common algebraic errors. For the equalities stated below assume that x and y stand for real numbers. Assume that any denominators are non-zero. Mark the equalities with T (true) if they are true for all values of x and y, and F (false) otherwise. 1 2a 1 4 ab. (correct) • 16aˆ11qˆ8 • • • • • • • • Answer(s) submitted: • N • N • = • = Simplify the following expression. 4a3 q2 −2a4 q3 1 2b Answer(s) submitted: • F • T • F • F (correct) 1 9. (1 point) 6. (1 point) Match the expressions below with the letters labeling their equivalent expressions. You must get all of the answers correct to receive credit. 1. 2. Change the radical r 3 8 y y + x−1 y y − x−1 y x x−y √ into simplest radical form AB C, where A, B, and C are all integers. Answer: A = ,B= , and C = 1 y2 Answer(s) submitted: − x12 x 3. y − y x + x y • 1 • 4 • 6 x x−2 y3 B. 2 y + x2 C. −yx A. (correct) 10. (1 point) Express the number Answer(s) submitted: • A • C • B −1 as a reduced fraction. Answer: (correct) 7. (1 point) Note: You cannot use any operations except division (/) and negation (-). Assume that a and b represent positive real numbers. Simplify the expression √ −5 20a7 b2 √ into the simplest radical form A C, where A and C are either integers or monomials. Answer: A = and C = Answer(s) submitted: • 16/9 (correct) 11. (1 point) Simplify each expression as much as possible √ and leave it without radicals. (a) √w6 x4 = 3 (b) p27w6 = (c) p49x4 y6p = (d) 8w7 y2 2y8 w5 = Answer(s) submitted: • -10baˆ3 • 5a Answer(s) submitted: (correct) 8. (1 point) • • • • Find the product √ √ 3 3 (8 6)(2 9) (wˆ3)(xˆ2) 3wˆ2 7xˆ2yˆ3 4wˆ6yˆ5 (correct) √ and express your answer in simplest radical form A 3 C, where A and C are integers. A= 2−4 3−2 12. (1 point) Write the expression as an equivalent expression in the form xn . Simplify your answer as much as possible, and enter your answer as a fraction. and C = 1 = xn for n = x7 Answer(s) submitted: Answer(s) submitted: • 48 • 2 • -7 (correct) (correct) 2 help (fractions) 13. (1 point) Rationalize the denominator. 17. (1 point) Factor the expression in a way that the coefficients of x are positive. 2+w √ √ = w− q 2x2 + x − 6. Factors (separate by commas): Type an exact answer using radical notation if necessary. Help: To enter √ the square root of a number use sqrt(). For example, to give 7x as an answer, you would type sqrt(7x). If you mistakenly type sqrt 7x instead, Webwork will take this to √ √ mean x 7, not 7x. That is, you MUST put parenthesis around everything that you want to take the square root of. You have 1 attempt(s) remaining before you will receive a new version of this problem. Answer(s) submitted: • (2x-3),(x+2) (correct) 18. (1 point) Factor the given polynomial 2y2 − 2 = Answer(s) submitted: • (2+w)(sqrt(w)+sqrt(q)) • w-q If the expression cannot be factored then answer with prime. (correct) Answer(s) submitted: 14. (1 point) • 2(y-1)(y+1) Simplify. Assume that all expressions (correct) under radicals represent nonnegative numbers. √ √ 3r − 7 3r + 7 = Write your answer using radical notation if necessary. Help: Click here for help writing exponents and square roots. 19. (1 point) Factor the given polynomial 9y2 + 6y + 1 = Answer(s) submitted: • 3r-49 If the expression cannot be factored then answer with prime. (correct) Answer(s) submitted: 15. (1 point) • (3y+1)ˆ2 Find the absolute value of the following numbers. (correct) 20. (1 point) a. |3| = Factor the given polynomial b. |−3| = 8x10 + 12x9 + 4x8 = c. −|3| = If the expression cannot be factored then answer with prime. d. −|−3| = Answer(s) submitted: • 4xˆ8(2x+1)(x+1) Answer(s) submitted: • 3 • 3 • -3 • -3 (correct) 21. (1 point) Factor the given polynomial (correct) 16. (1 point) r3 + 64 = Factor by grouping If the expression cannot be factored then answer with prime. 7ax − 7bx − 3ay + 3by. Factors (separate by commas): Answer(s) submitted: Answer(s) submitted: • (a-b),(7x-3y) • (r+4)(rˆ2-4r+16) (correct) (correct) 3 22. (1 point) 24. (1 point) (a) Factor the expression x4 − 16. If it plify if possible. Assume any factors you cancel are not zero. cannot be factored, enter NONE. help (formulas) 12 5c = 3 25c (b) Solve the equation x4 − 16 = 0. If there is more than one correct answer, enter your answers as a comma separated list. If there are no solutions, enter NONE. x= help (numbers) Answer(s) submitted: • 20 • 1 Answer(s) submitted: • (xˆ2+4)(x-2)(x+2) • 2,-2 (correct) (correct) 23. (1 point) Perform the indicated operation, and sim- 25. (1 point) Simplify the expression 3x3 − 1x2 − 10x 4x2 − 14x + 12 and give your answer in the form of f (x) g(x) Simplify the following expression. Assume any factors you cancel are not zero. 9 8 + s t = st where f (x) and g(x) are polynomials with no common factors. Your answer for the function f (x) is : Your answer for the function g(x) is : Answer(s) submitted: Answer(s) submitted: • x(3x+5) • 2(2x-3) • 9t+8s • sˆ2tˆ2 (correct) (correct) Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America 4