Problem 1SP: List all possible rational Zeros. fx=4x4+5x37x2+8 Problem 2SP: Find the zeros. fx=x3x24x2 Problem 3SP Problem 4SP Problem 5SP: Given fx=x42x3+28x24x+52, and that 1+5i is a zero of fx, a. Find the zeros b. Factor fx as a product... Problem 6SP: a. Find a third-degree polynomial fx with integer coefficient and with zeros of 2+iand43. b. Find a... Problem 7SP: Determine the number of possible positive and negative real zeros. fx=4x5+6x3+2x2+6 Problem 8SP: Determine the number of possible positive and negative real zeros. gx=8x85x7+3x5x23x+1 Problem 9SP Problem 10SP: Find the zeros and their multiplicities. fx=x5+6x32x227x18 Problem 1PE: The of a polynomial fx are the solutions (or roots) of the equation fx=0. Problem 2PE: If fx is a polynomial of degree n1 with complex coefficients, then fx has exactly complex zeros,... Problem 3PE: The conjugate zeros theorem states that if fx is a polynomial with real coefficient, and if a+bi is... Problem 4PE: A real number b is called an bound of the real zeros of a polynomial fx if all real zeros of fx are... Problem 5PE: A real number a is called a lower bound of the real zeros of a polynomial fx if all real zeros of fx... Problem 6PE: Explain why the number 7 cannot be a rational zero of the polynomial fx=2x3+5x2x+6. Problem 7PE: For Exercises 7-12, list the possible rational zeros. (See Example 1) fx=x52x3+7x2+4 Problem 8PE Problem 9PE: For Exercises 7-12, list the possible rational zeros. (See Example 1) hx=4x4+9x3+2x6 Problem 10PE: For Exercises 7-12, list the possible rational zeros. (See Example 1) kx=25x7+22x43x2+10 Problem 11PE: For Exercises 7-12, list the possible rational zeros. (See Example 1) mx=12x6+4x33x2+8 Problem 12PE: For Exercises 7-12, list the possible rational zeros. (See Example 1) nx=16x47x3+2x+6 Problem 13PE Problem 14PE: Which of the following is not a possible zero of fx=4x52x3+10? 3,5,52,32 Problem 15PE Problem 16PE: For Exercises 15-16, find all the rational zeros. qx=x4+x37x25x+10 Problem 17PE Problem 18PE Problem 19PE: For Exercises 17-28, find all the zeros. (See Example 2-4) fx=x37x2+6x+20 Problem 20PE: For Exercises 17-28, find all the zeros. (See Example 2-4) gx=x37x2+14x6 Problem 21PE Problem 22PE Problem 23PE Problem 24PE: For Exercises 17-28, find all the zeros. (See Example 2-4) nx=2x49x35x257x45 Problem 25PE: For Exercises 17-28, find all the zeros. (See Example 2-4) qx=x34x22x+20 Problem 26PE Problem 27PE: For Exercises 17-28, find all the zeros. (See Example 2-4) tx=x4x290 Problem 28PE: For Exercises 17-28, find all the zeros. (See Example 2-4) vx=x412x213 Problem 29PE: Given a polynomial fx of degree n1, the fundamental theorem of algebra guarantees at least complex... Problem 30PE Problem 31PE: If fx is a polynomial with real coefficients and zeros of 5 (multiplicity 2), 1 (multiplicity 1),... Problem 32PE: If gx is a polynomial with real coefficients and zeros of 4 (multiplicity 3), 6 (multiplicity 2),... Problem 33PE: For Exercises 33-38, a polynomial fx and one or more of its zeros is given. a. Find all the zeros.... Problem 34PE: For Exercises 33-38, a polynomial fx and one or more of its zeros is given. a. Find all the zeros.... Problem 35PE: For Exercises 33-38, a polynomial fx and one or more of its zeros is given. a. Find all the zeros.... Problem 36PE Problem 37PE Problem 38PE: For Exercises 33-38, a polynomial fx and one or more of its zeros is given. a. Find all the zeros.... Problem 39PE: For Exercises 39-48, write a polynomial fx that satisfies the given conditions. (See Example 6)... Problem 40PE: For Exercises 39-48, write a polynomial fx that satisfies the given conditions. (See Example 6)... Problem 41PE: For Exercises 39-48, write a polynomial fx that satisfies the given conditions. (See Example 6)... Problem 42PE: For Exercises 39-48, write a polynomial fx that satisfies the given conditions. (See Example 6)... Problem 43PE: For Exercises 39-48, write a polynomial fx that satisfies the given conditions. (See Example 6)... Problem 44PE: For Exercises 39-48, write a polynomial fx that satisfies the given conditions. (See Example 6)... Problem 45PE Problem 46PE: For Exercises 39-48, write a polynomial fx that satisfies the given conditions. (See Example 6)... Problem 47PE: For Exercises 39-48, write a polynomial fx that satisfies the given conditions. (See Example 6)... Problem 48PE: For Exercises 39-48, write a polynomial fx that satisfies the given conditions. (See Example 6)... Problem 49PE: For Exercises 49-56, determine the number of possible positive and negative real zeros for the given... Problem 50PE: For Exercises 49-56, determine the number of possible positive and negative real zeros for the given... Problem 51PE Problem 52PE: For Exercises 49-56, determine the number of possible positive and negative real zeros for the given... Problem 53PE: For Exercises 49-56, determine the number of possible positive and negative real zeros for the given... Problem 54PE: For Exercises 49-56, determine the number of possible positive and negative real zeros for the given... Problem 55PE: For Exercises 49-56, determine the number of possible positive and negative real zeros for the given... Problem 56PE: For Exercises 49-56, determine the number of possible positive and negative real zeros for the given... Problem 57PE: For Exercises 57-58, use Descartes’ rule of signs to determine the total number of real zeros and... Problem 58PE: For Exercises 57-58, use Descartes’ rule of signs to determine the total number of real zeros and... Problem 59PE: For Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given... Problem 60PE: For Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given... Problem 61PE: For Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given... Problem 62PE: For Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given... Problem 63PE: For Exercises 59-64, (See Example 9) a. Determine if the upper bound theorem identifies the given... Problem 64PE Problem 65PE: For Exercises 65-68, determine if the statement is true or false. If a statement is false, explain... Problem 66PE: For Exercises 65-68, determine if the statement is true or false. If a statement is false, explain... Problem 67PE: For Exercises 65-68, determine if the statement is true or false. If a statement is false, explain... Problem 68PE: For Exercises 65-68, determine if the statement is true or false. If a statement is false, explain... Problem 69PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 70PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 71PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 72PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 73PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 74PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 75PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 76PE Problem 77PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 78PE Problem 79PE Problem 80PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 81PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 82PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 83PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 84PE: For Exercises 69-84, find the zeros and their multiplicities. Consider using Descartes rule of signs... Problem 85PE: For Exercises 85-90, determine if the statement is true or false. If a statement is false, explain... Problem 86PE: For Exercises 85-90, determine if the statement is true or false. If a statement is false, explain... Problem 87PE: For Exercises 85-90, determine if the statement is true or false. If a statement is false, explain... Problem 88PE Problem 89PE: For Exercises 85-90, determine if the statement is true or false. If a statement is false, explain... Problem 90PE: For Exercises 85-90, determine if the statement is true or false. If a statement is false, explain... Problem 91PE: Given that xc divides evenly into a polynomial fx , which statements are true?... Problem 92PE: a. Use the quadratic formula to solve x27x+5=0. b. Write x27x+5 as a product of linear factors. Problem 93PE: a. Use the intermediate value theorem to show that fx=2x27x+4 has a real zero on the interval 2,3.... Problem 94PE: Show that xa is a factor of xnan for any positive integer n and constant a. Problem 95PE: Explain why a polynomial with real coefficients of degree 3 must have at least one real zero. Problem 96PE: Why is it not necessary to apply the rational zero theorem, Descartes’ rule of signs, or the upper... Problem 97PE Problem 98PE: Explain why the fundamental theorem of algebra does not apply to fx=x+3. That is, no complex number... Problem 99PE: Let n be a positive even integer. Determine the greatest number of possible nonreal zeros of fx=xn1. Problem 100PE: Let n be a positive odd integer. Determine the greatest number of possible nonreal zeros of fx=xn1. Problem 101PE: The front face of a tent is triangular and the height of the triangle is two-thirds of the base. The... Problem 102PE: An underground storage tank for gasoline is in the shape of a right circular cylinder with... Problem 103PE: A food company originally sells cereal in boxes with dimensions 10 in. by 7 in. by 2.5 in. To make... Problem 104PE Problem 105PE: A rectangle is bounded by the x-axis and a parabola defined by y=4x2 . What are the dimensions of... Problem 106PE: A rectangle is bounded by the parabola defined by y=x2 the x-axis, and the line x=5 as shown in the... Problem 107PE: For Exercises 107-110, a. Factor the polynomial over the set real numbers. b. Factor the polynomial... Problem 108PE: For Exercises 107-110, a. Factor the polynomial over the set real numbers. b. Factor the polynomial... Problem 109PE Problem 110PE: For Exercises 107-110, a. Factor the polynomial over the set real numbers. b. Factor the polynomial... Problem 111PE: Find all fourth roots of 1, by solving the equation x4=1. Problem 112PE: Find all sixth roots of 1, by solving the equation x6=1. Problem 113PE Problem 114PE Problem 115PE: For Exercises 115-116, use the formula x=n22+m33+n23n22+m33n23 To find a solution to the equation... Problem 116PE: For Exercises 115-116, use the formula x=n22+m33+n23n22+m33n23 To find a solution to the equation... format_list_bulleted
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