01:52Finding zeros and their multiplicities of a polynomial in factored formlarryschmidt799views1rank1comments
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+1260views4rank
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+x286views6rank
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+2438views3rank
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+7x3550views2rank
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+1648views2rank
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+18x2273views3rank
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)452views3rank
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+2x439views3rank
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+1258views2rank
Multiple ChoiceThe given term represents the leading term of some polynomial function. Determine the end behavior and the maximum number of turning points. 4x54x^54x5263views1rank
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=5x^2+6x^3520views
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 x264views
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/x210views
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+5246views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/x^3260views
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^4223views
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/3469views
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 + 2x395views
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^2571views
Textbook QuestionIn Exercises 11–14, identify which graphs are not those of polynomial functions. 265views
Textbook QuestionIn Exercises 11–14, identify which graphs are not those of polynomial functions. 373views
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)^4-3211views
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?341views
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 + 9293views
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+9308views
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+4212views
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^3405views
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+4491views
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-1295views
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+3387views
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+9846views
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^2-1235views
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^3-1321views
Textbook QuestionIn Exercises 25–26, graph each polynomial function. f(x) = 2x^2(x - 1)^3(x + 2)234views
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^2-2323views
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)^2579views
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)^2304views
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-2466views
Textbook QuestionIn Exercises 25–26, graph each polynomial function. f(x) = -x^3(x + 4)^2(x-1)261views
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^10305views
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)^3238views
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^4217views
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−28561views
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)466views
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)257views
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 2267views
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 1294views
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)^2260views
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 3424views
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)^2254views
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)^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+x^2−2x+1; between -3 and -2237views
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-5331views
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-36172views
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 - 5328views
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+2x233views
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 3262views
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^2185views
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 + 3328views
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)236views
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+6244views
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 - 7649views
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-2203views
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 + 1352views
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+8244views
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 10x7199views
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-6233views
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 -9x6268views
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 2387views
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 1360views
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 2359views
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 1364views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)218views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)359views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)^2(x-5)^2269views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)(x-5)211views
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 2192views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)(x-5)261views
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 1210views
Textbook QuestionFor each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)^2(x-5)^2189views
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 -2366views
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 -1271views
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 1184views
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 -2261views
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 2181views
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 -3196views
Textbook QuestionFind a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.) 313views
Textbook QuestionFind a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.) 560views
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]414views
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]287views
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]700views
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]726views
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.^3.202views
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.185views
Textbook QuestionExercises 107–109 will help you prepare for the material covered in the next section. Factor: x^3+3x^2−x−3240views
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.235views