01:52Finding zeros and their multiplicities of a polynomial in factored formlarryschmidt622views1rank1comments
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+1190views1rank
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+x226views6rank
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+2298views2rank
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+7x3332views1rank
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+1424views2rank
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+18x2193views4rank
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)320views2rank
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+2x269views2rank
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+1189views2rank
Multiple ChoiceThe given term represents the leading term of some polynomial function. Determine the end behavior and the maximum number of turning points. 4x54x^54x5215views1rank
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=5x^2+6x^3430views
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 x204views
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/x170views
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+5195views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/x^3209views
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^4171views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/3373views
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 + 2x288views
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^2429views
Textbook QuestionIn Exercises 11–14, identify which graphs are not those of polynomial functions. 194views
Textbook QuestionIn Exercises 11–14, identify which graphs are not those of polynomial functions. 260views
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)^4-3148views
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?225views
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 + 9229views
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+9216views
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+4146views
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^3302views
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+4368views
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-1213views
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+3300views
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+9641views
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^2-1171views
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^3-1236views
Textbook QuestionIn Exercises 25–26, graph each polynomial function. f(x) = 2x^2(x - 1)^3(x + 2)175views
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^2-2237views
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)^2447views
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)^2208views
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-2346views
Textbook QuestionIn Exercises 25–26, graph each polynomial function. f(x) = -x^3(x + 4)^2(x-1)200views
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^10217views
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)^3192views
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^4168views
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−28418views
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)324views
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)189views
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 2215views
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 1236views
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)^2192views
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 3320views
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)^2195views
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)^2170views
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 -2186views
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-5246views
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-36140views
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 - 5236views
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+2x174views
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 3210views
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^2141views
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 + 3245views
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)173views
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+6194views
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 - 7504views
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-2165views
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 + 1286views
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+8200views
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 10x7151views
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-6192views
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 -9x6192views
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 2299views
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 1282views
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 2291views
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 1277views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)156views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)242views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)^2209views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)(x-5)149views
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 2143views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)(x-5)205views
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 1158views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)^2148views
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 -2255views
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 -1199views
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 1145views
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 -2212views
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 2138views
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 -3161views
Textbook QuestionFind a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.) 213views
Textbook QuestionFind a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.) 417views
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]306views
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]232views
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]556views
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]481views
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.^3.156views
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.144views
Textbook QuestionExercises 107–109 will help you prepare for the material covered in the next section. Factor: x^3+3x^2−x−3192views
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.178views