01:52Finding zeros and their multiplicities of a polynomial in factored formlarryschmidt611views1rank1comments
Multiple ChoiceDetermine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. f(x)=4x3+12x−1−2x+1f\left(x\right)=4x^3+\frac12x^{-1}-2x+1f(x)=4x3+21x−1−2x+1188views
Multiple ChoiceDetermine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. f(x)=2+xf\left(x\right)=2+xf(x)=2+x224views5rank
Multiple ChoiceDetermine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. f(x)=3x2+5x+2f\left(x\right)=3x^2+5x+2f(x)=3x2+5x+2284views1rank
Multiple ChoiceDetermine the end behavior of the given polynomial function. f(x)=x2+4x+x+7x3f\left(x\right)=x^2+4x+x+7x^3f(x)=x2+4x+x+7x3317views
Multiple ChoiceMatch the given polynomial function to its graph based on end behavior. f(x)=−2x3+x2+1f\left(x\right)=-2x^3+x^2+1f(x)=−2x3+x2+1400views1rank
Multiple ChoiceFind the zeros of the given polynomial function and give the multiplicity of each. State whether the graph crosses or touches the x-axis at each zero. f(x)=2x4−12x3+18x2f\left(x\right)=2x^4-12x^3+18x^2f(x)=2x4−12x3+18x2187views2rank
Multiple ChoiceFind the zeros of the given polynomial function and give the multiplicity of each. State whether the graph crosses or touches the x-axis at each zero. f(x)=x2(x−1)3(2x+6)f\left(x\right)=x^2\left(x-1\right)^3\left(2x+6\right)f(x)=x2(x−1)3(2x+6)310views1rank
Multiple ChoiceDetermine the maximum number of turning points for the given polynomial function. f(x)=6x4+2xf\left(x\right)=6x^4+2xf(x)=6x4+2x258views1rank
Multiple ChoiceBased ONLY on the maximum number of turning points, which of the following graphs could NOT be the graph of the given function? f(x)=x3+1f\left(x\right)=x^3+1f(x)=x3+1184views1rank
Multiple ChoiceThe given term represents the leading term of some polynomial function. Determine the end behavior and the maximum number of turning points. 4x54x^54x5208views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=5x^2+6x^3423views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. g(x)=7x^5−πx^3+1/5 x202views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. h(x)=7x^3+2x^2+1/x168views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=x^1/2 −3x^2+5190views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/x^3208views
Textbook QuestionGraph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. See Example 1. ƒ(x)=2x^4170views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/3362views
Textbook QuestionIn Exercises 10–13, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] f(x) = -x^3 + x^2 + 2x285views
Textbook QuestionIn Exercises 10–13, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] f(x) = x^6 -6x^4 + 9x^2421views
Textbook QuestionIn Exercises 11–14, identify which graphs are not those of polynomial functions. 193views
Textbook QuestionIn Exercises 11–14, identify which graphs are not those of polynomial functions. 249views
Textbook QuestionGraph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. See Example 1. ƒ(x)=1/3(x+3)^4-3146views
Textbook QuestionGraph the following on the same coordinate system. (a) y = x^2 (b) y = 3x^2 (c) y = 1/3x^2 (d) How does the coefficient of x2 affect the shape of the graph?220views
Textbook QuestionIn Exercises 19–24, (a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Determine whether the graph has y-axis symmetry, origin symmetry, or neither. (c) Graph the function. f(x) = x^3 - x^2 - 9x + 9227views
Textbook QuestionIn Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. f(x)=5x^3+7x^2−x+9214views
Textbook QuestionGraph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. See Example 1. ƒ(x)=1/2(x-2)^2+4144views
Textbook QuestionIn Exercises 19–24, (a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Determine whether the graph has y-axis symmetry, origin symmetry, or neither. (c) Graph the function. f(x) = 4x - x^3297views
Textbook QuestionUse an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=5x^5+2x^3-3x+4358views
Textbook QuestionUse an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=-x^3-4x^2+2x-1207views
Textbook QuestionIn Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. f(x)=11x^4−6x^2+x+3297views
Textbook QuestionIn Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. f(x)=−5x^4+7x^2−x+9626views
Textbook QuestionUse an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=-4x^3+3x^2-1167views
Textbook QuestionUse an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=4x^7-x^5+x^3-1231views
Textbook QuestionIn Exercises 25–26, graph each polynomial function. f(x) = 2x^2(x - 1)^3(x + 2)173views
Textbook QuestionUse an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=9x^6-3x^4+x^2-2234views
Textbook QuestionIn Exercises 25–32, find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=2(x−5)(x+4)^2438views
Textbook QuestionIn Exercises 25–32, find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=3(x+5)(x+2)^2205views
Textbook QuestionUse an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=10x^6-x^5+2x-2337views
Textbook QuestionIn Exercises 25–26, graph each polynomial function. f(x) = -x^3(x + 4)^2(x-1)195views
Textbook QuestionUse an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=3+2x-4x^2-5x^10214views
Textbook QuestionIn Exercises 25–32, find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=−3(x+1/2)(x−4)^3189views
Textbook QuestionUse an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=7+2x-5x^2-10x^4165views
Textbook QuestionIn Exercises 25–32, find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=x^3+7x^2−4x−28409views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=-2x(x-3)(x+2)313views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=-x(x+1)(x-1)181views
Textbook QuestionIn Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x^3−x−1; between 1 and 2213views
Textbook QuestionIn Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x^3−4x^2+2; between 0 and 1233views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=(3x-1)(x+2)^2184views
Textbook QuestionIn Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x^4+6x^3−18x^2; between 2 and 3309views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=(4x+3)(x+2)^2192views
Textbook QuestionDetermine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = (x + 3)^2167views
Textbook QuestionIn Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x^3+x^2−2x+1; between -3 and -2184views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=x^3+5x^2-x-5243views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=x^3+x^2-36x-36136views
Textbook QuestionDetermine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = -(x - 2)^2 - 5229views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=-x^3+x^2+2x173views
Textbook QuestionIn Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=3x^3−8x^2+x+2; between 2 and 3209views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=-3x^4-5x^3+2x^2140views
Textbook QuestionDetermine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = x^2 - 4x + 3240views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=2x^3(x^2-4)(x-1)172views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=2x^3-5x^2-x+6190views
Textbook QuestionDetermine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = -2x^2 - 8x - 7481views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=2x^4+x^3-6x^2-7x-2163views
Textbook QuestionDetermine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = -3x^2 + 18x + 1280views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=3x^4-7x^3-6x^2+12x+8196views
Textbook QuestionIf the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a)domain (b)range (c)end behavior (d)number of zeros (e)number of turning points 10x7150views
Textbook QuestionGraph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=x^4+3x^3-3x^2-11x-6190views
Textbook QuestionIf the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a)domain (b)range (c)end behavior (d)number of zeros (e)number of turning points -9x6188views
Textbook QuestionUse the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. See Example 5. ƒ(x)=3x^2-x-4; 1 and 2295views
Textbook QuestionUse the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. See Example 5. ƒ(x)=-2x^3+5x^2+5x-7; 0 and 1277views
Textbook QuestionUse the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. See Example 5. ƒ(x)=2x^4-4x^2+4x-8; 1 and 2285views
Textbook QuestionUse the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. See Example 5. ƒ(x)=x^4-4x^3-x+3; 0.5 and 1272views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)155views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)235views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)^2206views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)(x-5)148views
Textbook QuestionShow that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^4-x^3+3x^2-8x+8; no real zero greater than 2142views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)(x-5)204views
Textbook QuestionShow that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=2x^5-x^4+2x^3-2x^2+4x-4; no real zero greater than 1156views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)^2147views
Textbook QuestionShow that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^4+x^3-x^2+3; no real zero less than -2245views
Textbook QuestionShow that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^5+2x^3-2x^2+5x+5; no real zero less than -1198views
Textbook QuestionShow that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=3x^4+2x^3-4x^2+x-1; no real zero greater than 1144views
Textbook QuestionShow that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=3x^4+2x^3-4x^2+x-1; no real zero less than -2211views
Textbook QuestionShow that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^5-3x^3+x+2; no real zero greater than 2137views
Textbook QuestionShow that the real zeros of each polynomial function satisfy the given conditions. See Example 6. ƒ(x)=x^5-3x^3+x+2; no real zero less than -3160views
Textbook QuestionFind a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.) 210views
Textbook QuestionFind a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.) 408views
Textbook QuestionUse a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=2x^3-5x^2-x+1; [-1, 0]299views
Textbook QuestionUse a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=2x^3-5x^2-x+1; [1.4, 2]225views
Textbook QuestionUse a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=x^3+4x^2-8x-8; [-3.8, -3]544views
Textbook QuestionUse a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=x^4-7x^3+13x^2+6x-28; [-1, 0]470views
Textbook QuestionThe following exercises are geometric in nature and lead to polynomial models. Solve each problem. A standard piece of notebook paper measuring 8.5 in. by 11 in. is to be made into a box with an open top by cutting equal-size squares from each cor-ner and folding up the sides. Let x represent the length of a side of each such square in inches. Use the table feature of a graphing calculator to do the following. Round to the nearest hundredth. Determine when the volume of the box will be greater than 40 in.^3.154views
Textbook QuestionThe following exercises are geometric in nature and lead to polynomial models. Solve each problem. A standard piece of notebook paper measuring 8.5 in. by 11 in. is to be made into a box with an open top by cutting equal-size squares from each cor-ner and folding up the sides. Let x represent the length of a side of each such square in inches. Use the table feature of a graphing calculator to do the following. Round to the nearest hundredth. Find the maximum volume of the box.142views
Textbook QuestionExercises 107–109 will help you prepare for the material covered in the next section. Factor: x^3+3x^2−x−3190views
Textbook QuestionExercises 107–109 will help you prepare for the material covered in the next section. Determine whether f(x)=x^4−2x^2+1 is even, odd, or neither. Describe the symmetry, if any, for the graph of f.176views