Problem 1SP: Use long division to divide 4x323x+32x5. Problem 2SP: Use long division to divide. 17x+5x23x3+2x4x2+3 Problem 3SP: Use long division to divide. 3x214x+15x3 Problem 4SP: Use synthetic division to divide. 4x328x7x3 Problem 5SP: Use synthetic division to divide. 3x+7x3+5+2x4x+1 Problem 6SP: Given fx=x4+x36x25x15, use the remainder theorem to evaluate a.f5b.f3 Problem 7SP: Use the remainder theorem to determine if the given number, c, is a zero of the function.... Problem 8SP: Use the factor theorem to determine if the given polynomials are factors of fx=2x413x3+10x225x+6.... Problem 9SP: a. Factor fx=2x3+7x214x40, given that 4 is a zero of f . b. Solve the equation. 2x3+7x214x40=0 Problem 10SP: Write a polynomial fx of degree 3 that has the zeros 13,3,and3. Problem 1PE: Given the division algorithm, identify the polynomials representing the dividend, divisor, quotient,... Problem 2PE: Given 2x35x26x+1x3=2x2+x3+8x3, use the division algorithm to check the result. Problem 3PE: The remainder theorem indicates that if a polynomial fx is divided by xc, then the remainder is . Problem 4PE: Given a polynomial fx, the factor theorem indicates that if fc=0,thenxc is a of fx, furthermore, if... Problem 5PE: Answer true or false. If 5 is a zero of a polynomial, then x5 is a factor of the polynomial. Problem 6PE: Answer true or false. If x+3 is a factor of a polynomial, then 3 is a zero of the polynomial. Problem 7PE: For Exercises 7-8, (See Example 1) a. Use long division to divide. b. Identify the dividend,... Problem 8PE Problem 9PE: For Exercises 9-22, use long division to divide. (See Example 1-3) 3x311x210x4 Problem 10PE: For Exercises 9-22, use long division to divide. (See Example 1-3) 2x37x265x5 Problem 11PE: For Exercises 9-22, use long division to divide. (See Example 1-3) 8+30x27x212x3+4x4x+2 Problem 12PE: For Exercises 9-22, use long division to divide. (See Example 1-3) 4828x+20x2+17x3+3x4x+3 Problem 13PE: For Exercises 9-22, use long division to divide. (See Example 1-3) 20x2+6x4162x+4 Problem 14PE: For Exercises 9-22, use long division to divide. (See Example 1-3) 60x2+8x41082x6 Problem 15PE: For Exercises 9-22, use long division to divide. (See Example 1-3) x5+4x4+18x220x10x2+5 Problem 16PE: For Exercises 9-22, use long division to divide. (See Example 1-3) x52x4+x38x18x23 Problem 17PE: For Exercises 9-22, use long division to divide. (See Example 1-3) 6x4+3x37x2+6x52x2+x3 Problem 18PE Problem 19PE Problem 20PE: For Exercises 9-22, use long division to divide. (See Example 1-3) x3+64x+4 Problem 21PE: For Exercises 9-22, use long division to divide. (See Example 1-3) 5x32x2+32x1 Problem 22PE: For Exercises 9-22, use long division to divide. (See Example 1-3) 2x3+x2+13x+1 Problem 23PE: For Exercises 23-26, consider the division of two polynomials: fxxc. The result of the synthetic... Problem 24PE Problem 25PE: For Exercises 23-26, consider the division of two polynomials: fxxc. The result of the synthetic... Problem 26PE Problem 27PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5)... Problem 28PE Problem 29PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5) 5x217x12x4 Problem 30PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5) 2x2+x21x3 Problem 31PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5)... Problem 32PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5)... Problem 33PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5)... Problem 34PE Problem 35PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5) x5+32x+2 Problem 36PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5) x481x+3 Problem 37PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5)... Problem 38PE: For Exercises 27-38, use synthetic division to divide the polynomials. (See Example 4-5)... Problem 39PE: The value f6=39 for a polynomial fx . What can be concluded about the remainder or quotient of... Problem 40PE: Given a polynomial fx, the quotient fxx2 has a reminder of 12. What is the value of f2? Problem 41PE: Given fx=2x45x3+x27, a. Evaluate f4 . b. Determine the remainder when fx is divided by x4. Problem 42PE: Given gx=3x5+2x4+6x2x+4, a. Evaluate g2 b. Determine the remainder when gx is divided by x2. Problem 43PE: For Exercises 43-46, use the remainder theorem to evaluate the polynomial for the given value of x.... Problem 44PE: For Exercises 43-46, use the remainder theorem to evaluate the polynomial for the given value of x.... Problem 45PE: For Exercises 43-46, use the remainder theorem to evaluate the polynomial for the given value of x.... Problem 46PE: For Exercises 43-46, use the remainder theorem to evaluate the polynomial for the given value of x.... Problem 47PE: For Exercises 47-54, use the reminder theorem to determine if the given number c is a zero of the... Problem 48PE: For Exercises 47-54, use the reminder theorem to determine if the given number c is a zero of the... Problem 49PE: For Exercises 47-54, use the reminder theorem to determine if the given number c is a zero of the... Problem 50PE: For Exercises 47-54, use the reminder theorem to determine if the given number c is a zero of the... Problem 51PE: For Exercises 47-54, use the reminder theorem to determine if the given number c is a zero of the... Problem 52PE Problem 53PE Problem 54PE: For Exercises 47-54, use the reminder theorem to determine if the given number c is a zero of the... Problem 55PE: For Exercises 55-60, use the factor theorem to determine if the given binomial is a factor of fx .... Problem 56PE: For Exercises 55-60, use the factor theorem to determine if the given binomial is a factor of fx .... Problem 57PE: For Exercises 55-60, use the factor theorem to determine if the given binomial is a factor of fx .... Problem 58PE: For Exercises 55-60, use the factor theorem to determine if the given binomial is a factor of fx .... Problem 59PE: For Exercises 55-60, use the factor theorem to determine if the given binomial is a factor of fx .... Problem 60PE Problem 61PE: Given gx=x414x2+45, a. Evaluate g5. b. Evaluate g5. c. Solve gx=0 . Problem 62PE: Given hx=x415x2+44, a. Evaluate h11. b. Evaluate h11. c. Solve hx=0 . Problem 63PE Problem 64PE Problem 65PE: a. Factor fx=2x3+x237x36, given that 1 is a zero. (See Example 9) b. Solve. 2x3+x237x36=0 Problem 66PE: a. Factor fx=3x3+16x25x50, given that 2 is a zero. b. Solve. 3x3+16x25x50=0 Problem 67PE: a. Factor fx=20x3+39x23x2, given that 14 is a zero. b. Solve. 20x3+39x23x2=0 Problem 68PE: a. Factor fx=8x318x211x+15, given that 34 is a zero. b. Solve. 8x318x211x+15=0 Problem 69PE: a. Factor fx=9x333x2+19x3, given that 3 is a zero. b. Solve. 9x333x2+19x3=0 Problem 70PE Problem 71PE: For Exercises 71-82, write a polynomial fx that meets the given conditions. Answers may vary. (See... Problem 72PE Problem 73PE Problem 74PE: For Exercises 71-82, write a polynomial fx that meets the given conditions. Answers may vary. (See... Problem 75PE Problem 76PE: For Exercises 71-82, write a polynomial fx that meets the given conditions. Answers may vary. (See... Problem 77PE: For Exercises 71-82, write a polynomial fx that meets the given conditions. Answers may vary. (See... Problem 78PE: For Exercises 71-82, write a polynomial fx that meets the given conditions. Answers may vary. (See... Problem 79PE Problem 80PE: For Exercises 71-82, write a polynomial fx that meets the given conditions. Answers may vary. (See... Problem 81PE Problem 82PE: For Exercises 71-82, write a polynomial fx that meets the given conditions. Answers may vary. (See... Problem 83PE Problem 84PE Problem 85PE: ... Problem 86PE: If a fifth-degree polynomial is divided by a second-degree polynomial, the quotient is a -degree... Problem 87PE: Determine if the statement is true or false: Zero is a zero of the polynomial 3x57x42x314. Problem 88PE: Determine if the statement is true or false: Zero is a zero of the polynomial 2x4+5x3+6x. Problem 89PE: Find m so that x+4 is a factor of 4x3+13x25x+m. Problem 90PE: Find m so that x+5 is a factor of 3x410x3+20x222x+m. Problem 91PE: Find m so that x+2 is a factor of 4x3+5x2+mx+2. Problem 92PE Problem 93PE Problem 94PE: For what value of r is the statement an identify? x25x8x2=x3+rx2 provided that x2 Problem 95PE: A metal block is formed from a rectangular solid with a rectangular piece cut out. a. Write a... Problem 96PE: A wedge is cut from a rectangular solid. a. Write a polynomial Vx that represents the volume of the... Problem 97PE: Under what circumstances can synthetic division be used to divide polynomials? Problem 98PE: How can the division algorithm be used to check the result of polynomial division? Problem 99PE: Given a polynomial fx and a constant c, state two methods by which the value fc can be computed. Problem 100PE: Write an informal explanation of the factor theorem. Problem 101PE: a. Factor fx=x35x2+x5 into factors of the form xc, given that 5 is a zero. b. Solve. x35x2+x5=0 Problem 102PE: a. Factor fx=x33x2+100x300 into factors of the form xc, given that 3 is a zero. b. Solve.... Problem 103PE: a. Factor fx=x4+2x32x26x3 into factors of the form xc, given that 1 is a zero. b. Solve.... Problem 104PE: a. Factor fx=x4+4x3x220x20 into factors of the form xc, given that 2 is a zero. b. Solve.... Problem 105PE: For Exercises 105-106, a. Use the graph to determine a solution to the given equation. b. Verify... Problem 106PE: For Exercises 105-106, a. Use the graph to determine a solution to the given equation. b. Verify... format_list_bulleted