01:52Finding zeros and their multiplicities of a polynomial in factored formlarryschmidt636views1rank1comments
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+1193views2rank
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+x230views6rank
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+2322views3rank
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+7x3351views2rank
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+1449views2rank
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+18x2205views3rank
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)334views2rank
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+2x284views1rank
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+1194views2rank
Multiple ChoiceThe given term represents the leading term of some polynomial function. Determine the end behavior and the maximum number of turning points. 4x54x^54x5218views2rank
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=5x^2+6x^3438views
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 x209views
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/x172views
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+5200views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/x^3215views
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^4176views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/3384views
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 + 2x297views
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^2443views
Textbook QuestionIn Exercises 11–14, identify which graphs are not those of polynomial functions. 201views
Textbook QuestionIn Exercises 11–14, identify which graphs are not those of polynomial functions. 272views
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)^4-3154views
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?241views
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 + 9237views
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+9224views
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+4153views
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^3311views
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+4379views
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-1222views
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+3309views
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+9667views
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^2-1178views
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^3-1246views
Textbook QuestionIn Exercises 25–26, graph each polynomial function. f(x) = 2x^2(x - 1)^3(x + 2)178views
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^2-2242views
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)^2461views
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)^2218views
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-2357views
Textbook QuestionIn Exercises 25–26, graph each polynomial function. f(x) = -x^3(x + 4)^2(x-1)205views
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^10222views
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)^3195views
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^4173views
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−28432views
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)344views
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)193views
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 2220views
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 1244views
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)^2200views
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 3329views
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)^2201views
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)^2175views
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 -2191views
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-5255views
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-36143views
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 - 5242views
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+2x180views
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 3216views
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^2143views
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 + 3254views
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)178views
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+6197views
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 - 7518views
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-2168views
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 + 1293views
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+8201views
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 10x7154views
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-6194views
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 -9x6202views
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 2311views
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 1290views
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 2298views
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 1284views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)162views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)254views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)^2213views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)(x-5)154views
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 2147views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)(x-5)212views
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 1163views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)^2152views
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 -2266views
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 -1207views
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 1146views
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 -2215views
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 2140views
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 -3162views
Textbook QuestionFind a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.) 223views
Textbook QuestionFind a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.) 430views
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]317views
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]235views
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]569views
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]509views
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.^3.160views
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.147views
Textbook QuestionExercises 107–109 will help you prepare for the material covered in the next section. Factor: x^3+3x^2−x−3196views
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.186views