Name: 20922CB8 V1 - Page 1 1) What is the quotient when x' - 2x2 - 9 is divided 6) Find the given quotient using Long Division of by x - 3? Polynomials [Show all work. ]: (4x3 - 5x2 - 16x + 20) + (4x - 5) A) x2 - x - 6 C) x2 + x - 6 B) x2 + x+ 3 D) x2 - 5x + 6 7) Find the given quotient using Long Division of Polynomials [Show all work. ]: 2) What is the quotient when ( + 513 - 272 + 10t -8) (3x3 - 7x2+ 15x -35)+ (3x - 7) is divided by (12 + 2)? A) 12t - 14 C) 12 - 5t + 3 B) 12 + 5t - 4 D) 12 - 31-2 Questions 8 through 11 refer to the following: Use Long Division of Polynomials to find the quotient q(x) and remainder R of the given expression. 3) When x3 - x2 - 7x + 17 is divided by x2 - 4x + 5, [Show all work.] the remainder is 8) 725 -2x4 -5x3+2-32+5 A) 2 B)O C) 3 D) 4 2-2 4) What is the remainder when 2x4 + 3x3 - x2 - 2 is 9) (323-17x2+15x-15) divided by x + 2? (z-5) A) 2 B) -8 C) -2 D) 4 10) (523+18x3+71-6) 5) What is the remainder when x* + 2x3 - 4x2 - 5 is (+3) divided by x + 3? A) -2 B) 4 C) 94 D) -1420922CB8 V1 - Page 2 11) (4x3-92+15x2-18) 16) Use Long Division of Polynomials to divide (x+2) x3 + x2 - 4x - 4 by x - 3. [Show all work. ] [Express the complete quotient in the form O + Questions 12 through 14 refer to the following: Use Long Division of Polynomials to divide f(x) by g(x). [Show all work. ] [Express function fin the 17) Use Long Division of Polynomials to divide form f(x) = (quotient)(divisor) + (remainder).] f(x) = 2x3 - 5x2 + x+ 2 by x -2. [Show all work. ] [Express function f in the form f(x) = (quotient) 12) f(x ) = (x3 -x2+ 2x+4) (divisor) + (remainder).] g(x) = (x -2) 18) 13) f(x) = (x5 - 4x3 + x) (a) Use long division to divide g(x) = (x+3) f(x) = 2x4+ 7x3 -4x2 -27x - 18 by x + 1. [Show all work. ] [Express function fin the form f(x) = (quotient)(divisor) + (remainder). ] (b) Is x + 1 a factor of function f? [Justify your answer.] 14) f(x) = (4x6 - 3x4 + x2 + 5) g(x) = (x - 1) 19) (a) Use long division to find the complete quotient for (3x' + 4x2+ x -2) (x + 1). 15) Use Long Division of Polynomials to divide [Show all work. ] 5x5 - 3x3 + 4x2 - 2x + 1 by x + 2. [Show all (b) Is x + 1 a factor of 3x3 + 4x2 + x - 2? work. ] [Express the complete quotient in the form [Justify your answer. ]20) If the remainder equals zero when a polynomial expression is divided by x - a, then A) x o is not a factor of the polynomial B) the polynomial must be of degree 2 C) the polynomial must be of degree 0 D) x a is a factor of the polynomial Questions 21 through 24 refer to the following: Use the division of polynomials to determine the polynomial, p(x), that satises the given equation. [Show of! work] 21) p(x)(4xz 3) =4x+5x4 +243 6 22) p(x)(x2-2)=x5 -?x2-4x+ l4 23) 2x? +3x5 -4x4+ 9= ptx)(2xz + 3) 24) x52x42x34x2+15x5=p(x)(x23x+1) 20922CBS v1 - Page 3 25) Use Long Division of Polynomials to determine the value of k that makes it + 3 a factor of x3 - 9x + k. [Show all work] 26) Use Long Division of Polynomials to determine the value of k that makes x = 2 a zero of 2x3 3x2 + x + k = 0. [Show a\" work] 27) Use Long Division of Polynomials to determine the value of k that makes x + 2 a factor of x3 + 5x2 + for + 4. [Show all work] 23) Use Long Division of Polynomials to determine the value of k such that x = -3 is a root of x3 - 4.x2 + for - 6 = 0. [Show a\" work] 29) Use Long Division of Polynomials to determine if x - 2 is a factor of the polynomial P(x) = x4 - 3x3 + 5x - 2. [Show all work] [Explain why or why not?] 30) Use Long Division of Polynomials to determine 35) What are the roots of the equation if x = -2 is a zero of P(x) = x# - 6x- - 10x + 3. 5x- - 7x + 1 = 0? [Show all work. ] [Explain why or why not? ] A) -7+v29 C) 7+ v29 10 10 B) 7+ V69 D) -71 169 10 10 31) Use Long Division of Polynomials to determine if x = 2 is a root of the equation 0=x +x - 4x -4. [Show all work. ] [Explain why or why not?] 36) What are the roots of the equation x2 + 3x - 5 = 0? A) -3+ VII C) -3+29 B) 3+ 29 D) 3+ VII 2 2 32) Use Long Division of Polynomials to verify that x - 2 is a factor of f(x) = 10x3 - 15x2 - 16x + 12. [Show all work. ] [Explain why or why not?] 37) What is the sum of the roots of the equation 2x2 - 3x +9= 0? A) - B)- D)- 33) (a) Use Long Division of Polynomials to show that (2x - 1) and (x + 2) are factors of f(x) = 4x4 - 31x2 -21x + 18. [Show all work.] (b) Write f(x) in factored form. 38) What is the sum of the roots of the equation 2x2 - 3x +4 = 0? A) 3 B)- C) 2 D) 2 34) (a) Use Long Division of Polynomials to show that (x - 2) and (x + 4) are factors of f(x) = x4 - 3x3 - 18x2+ 40x. [Show all work.] (b) Write f(x) in factored form.39) What is the sum of the roots of the equation 44) What is the sum (S) and the product (P) of the x- - 11x + 10 = 0? roots of the equation 2x2 - 4x + 1 = 0? A) -7 B) 10 C) 11 D) 7 A) S =-2, P= C) S= -4, P =1 B) S = J, P=2 D) S = 2, P = 40) What is the sum of the roots of the equation 3x2 = 9x + 1? 45) What are the sum (S) and the product (P) of the A) 3 B) 9 C) - D) -3 roots of the equation x2 + 2x - 35 = 0? A) S= 2, P=-35 C) S= -35, P = 2 B) S = 35, P=-2 D) S= -2, P=-35 41) What is the product of the roots of the equation 2x2 - 9x + 6 = 0? A) -9 B) 3 D) ; 46) If the sum of the roots of the equation x- + kx - 3 = 0 is equal to the product of the roots, the value of k is A) 3 B) -6 C) -3 D) 6 42) What is the product of the roots of the equation 2x2 - x - 2 = 0? A) 1 B) 2 C) -2 D) -1 47) For which equation is the sum of the roots equal to the product of the roots? A)x+x+1=0 C) x2 - 4x + 4 = 0 B) x2 - 8x - 4= 0 D) x2 + 3x - 6 = 0 43) What is the product of the roots of the equation -2x2 + 3x +8= 0? A) 3 B) -4 C) 3 D) 448) For which equation does the sum of the roots 53) Determine the sum and product of the roots of equal 3 and the product of the roots equal 4.5? x - 17 = 0. [Show all work. ] A) x2 + 3x - 9=0 C) 2x2 - 6x + 9= 0 B) 2x2 + 6x + 9 = 0 D) x2 - 3x +9=0 Questions 54 through 59 refer to the following: Find the sum and the product of the roots of the given 49) Which equation has roots whose sum is 3 and quadratic equation. [Show all work. ] whose product is -4? 54) 12 - 3y = 2y + 50 A) x2 - 3x - 4 = 0 C) x2 + 4x - 3= 0 B) x2 - 4x + 3 = 0 D) x2 + 3x - 4=0 55) 322 + 2 =72 50) Determine the sum and product of the roots of 3y2 - 2y + 12 = 0. [Show all work. ] 56) -3x2 = 6x - 1 51) Determine the sum and product of the roots of 3x - 4= -x2. [Show all work. ] 57) 2x2 - 5= -3x 52) Determine the sum and product of the roots of 12 = 4x - 3x2. [Show all work. ] 58) 4y2 = 8y - 1