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Questions and Answers of College Algebra

Use synthetic division to divide ƒ(x) by x - k for the given value of k. Then express ƒ(x) in the form ƒ(x) = (x - k)q(x) + r.ƒ(x) = -x3 + x2 + 3x - 2; k = 2
Use synthetic division to divide ƒ(x) by x - k for the given value of k. Then express ƒ(x) in the form ƒ(x) = (x - k)q(x) + r.ƒ(x) = x3 + 4x2 + 5x + 2; k = -2
Use synthetic division to divide ƒ(x) by x - k for the given value of k. Then express ƒ(x) in the form ƒ(x) = (x - k)q(x) + r.ƒ(x) = 2x3 + 3x2 - 16x + 10; k = -4
Use synthetic division to divide ƒ(x) by x - k for the given value of k. Then express ƒ(x) in the form ƒ(x) = (x - k)q(x) + r.ƒ(x) = 2x3 + x2 + x - 8; k = -1
Use synthetic division to perform each division. x7 + 1 x + 1
Use synthetic division to perform each division. х4 — 1 х — 1
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing.ƒ(x) = (x + 2)3 - 1
Use synthetic division to perform each division. -11x4 — 2х3 — 8х2 — 4 х+1
Use synthetic division to perform each division. -9х3 + 8x2 — 7х + 2 х — 2
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing.ƒ(x) = -(x + 1)3 + 1
Graph each function. Determine the largest open intervals of the domain over which each function is (a) Increasing (b) Decreasing. (x) = 12 x + -x + 1
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.-2x3 + x2 - 63; x + 3
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing.ƒ(x) = -x4 + 2
Use synthetic division to perform each division. x6 — Зх4 + 2х3 — 6х? — 5х + 3 бх? х+ 2
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. 2 f(x) ===x5 3
Use synthetic division to perform each division. x5 + 3x4 + 2.x³ + 2x² + 3x + 1 x +2
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.-x3 + 3x - 2; x + 2
Consider the graph of each quadratic function. Do the following.(a) Give the domain and range. (b) Give the coordinates of the vertex.(c) Give the equation of the axis. (d) Find the
Consider the graph of each quadratic function. Do the following.(a) Give the domain and range. (b) Give the coordinates of the vertex.(c) Give the equation of the axis. (d) Find the
Solve the problem.Find a value of k such that x - 4 is a factor of ƒ(x) = x3 - 2x2 + kx + 4.
Solve the problem.Find all zeros of ƒ(x) = 2x4 - x3 + 7x2 - 4x - 4, given that 1 and -2i are zeros.
Consider the graph of each quadratic function. Do the following.(a) Give the domain and range. (b) Give the coordinates of the vertex.(c) Give the equation of the axis. (d) Find the
Solve the problem.Is x + 1 a factor of ƒ(x) = x3 + 2x2 + 3x + 2?
Solve each problem.Use Descartes’ rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of ƒ(x) = x3 + 3x2 - 4x - 2.
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 39 and 40, also work part (c).ƒ(x) = 6x4 + 13x3 - 11x2 - 3x + 5(a) no zero greater than 1 (b)
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 39 and 40, also work part (c).ƒ(x) = 4x3 - 37x2 + 50x + 60(a) Between 2 and 3 (b) Between 7
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 39 and 40, also work part (c).ƒ(x) = 3x3 - 8x2 + x + 2(a) Between -1 and 0 (b) Between 2 and
Find all rational zeros of each function.ƒ(x) = 8x4 - 14x3 - 29x2 - 4x + 3
Find all rational zeros of each function.ƒ(x) = 2x3 - 9x2 - 6x + 5
Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given.0, 5, 1 + 2i
Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given.2, 4, -i
Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given. -2 + 5, -2- V5, -2, 1
Fill in the blank(s) to correctly complete each sentence.The graph of ƒ(x) = -2x2 - 6x + 5 opens down with y-intercept (0, ________), so it has x-intercept(s).
Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given. V3, - V (3, 2, 3
Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given.8, 2, 3
Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given.-1, 4, 7
Suppose the polynomial function ƒ has a zero at x = -3. Which of the following statements must be true?A. (3, 0) is an x-intercept of the graph of ƒ.B. (0, 3) is a y-intercept of the graph of ƒ.C.
Show that the real zeros of each polynomial function satisfy the given conditions.ƒ(x) = x4 - x3 + 3x2 - 8x + 8; no real zero greater than 2
Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given.ƒ(x) = x4 + x3 - 6x2 - 20x - 16; 3.2 and 3.3
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = 2x3 + 9x2 - 16x + 12; k = 1
In each scatter diagram, tell whether a linear or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, tell whether the
Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given.ƒ(x) = x4 - 4x3 - x + 3; 0.5 and 1
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = 2x3 - 6x2 - 9x + 4; k = 1
In each scatter diagram, tell whether a linear or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, tell whether the
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = (x2 + x - 2)5 (x - 1 + √3)2
Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given.ƒ(x) = 2x4 - 4x2 + 4x - 8; 1 and 2
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = x3 + 2x2 - x + 6; k = -3
Find a quadratic function f having the graph shown. (1,0) (-1, –12)
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = 5x2(x2 - 16)(x + 5)
Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given.ƒ(x) = 2x3 - 9x2 + x + 20; 2 and 2.5
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = x3 - 3x2 + 4x - 4; k = 2
Find a quadratic function f having the graph shown. y t1, 4) (0, 2)4
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = 3x(x - 2)(x + 3)(x2 - 1)
Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given.ƒ(x) = 2x3 - 5x2 - 5x + 7; 0 and 1
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = x2 + 4x - 5; k = -5
Find a quadratic function f having the graph shown. (-2, 3) х (0, –1)
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = (x + 1)2(x - 1)3(x2 - 10)
Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given.ƒ(x) = 3x2 - x - 4; 1 and 2
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = x2 + 2x - 8; k = 2
Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given.ƒ(x) = 2x2 - 7x + 4; 2 and 3
Find a quadratic function f having the graph shown. (0,0) (2, –1)
For each polynomial function, use the remainder theorem to find ƒ(k). f(x) = 6x³ – 31x² – 15x; k = - %3D
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = 24x3 + 40x2 - 2x - 12
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = 2x4 + x3 - 6x2 - 7x - 2
Several graphs of the quadratic function ƒ(x) = ax2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F.a < 0; b2 - 4ac > 0
For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = 2x5 - 10x3 - 19x2 - 50; k = 3
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = 6x3 + 17x2 - 31x - 12
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = 2x3 - 5x2 - x + 6
Several graphs of the quadratic function ƒ(x) = ax2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F.a < 0; b2 - 4ac < 0
For each polynomial function, use the remainder theorem to find ƒ(k). f(x) = 2x² + 10; k= iV5
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = x3 - x2 - 10x - 8
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = x2(x - 3)3(x + 1)
Several graphs of the quadratic function ƒ(x) = ax2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F.a > 0; b2 - 4ac < 0
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = x3 + 6x2 - x - 30
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = 2x3(x2 - 4)(x - 1)
Several graphs of the quadratic function ƒ(x) = ax2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F.a < 0; b2 - 4ac = 0 A.
For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = x2 - x + 3; k = 3 - 2i
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = x3 + 5x2 + 2x - 8
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = 3x4 + 5x3 - 2x2
The figure shows the graph of a quadratic function y = ƒ(x). Use it to answer each question.How many real solutions are there to the equation ƒ(x) = 4?
For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = x2 - 5x + 1; k = 2 + i
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = x3 - x2 - 2x
The figure shows the graph of a quadratic function y = ƒ(x). Use it to answer each question.How many real solutions are there to the equation ƒ(x) = 1?
For each polynomial function, one zero is given. Find all other zeros.ƒ(x) = x4 + 26x2 + 25; i
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = x3 + x2 - 36x - 36
The figure shows the graph of a quadratic function y = ƒ(x). Use it to answer each question.For what value of x is ƒ(x) as small as possible?
The figure shows the graph of a quadratic function y = ƒ(x). Use it to answer each question.What is the minimum value of ƒ(x)? 'y = f(x) (-3, 3) -3 3.
For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = x3 - 4x2 + 2x + 1; k = -1
For each polynomial function, one zero is given. Find all other zeros.ƒ(x) = x4 + 5x2 + 4; -i
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = x3 + 5x2 - x - 5
Graph each quadratic function. Give the (a) Vertex, (b) Axis, (c) Domain, (d) Range. Then determine (e) The largest open interval of the domain over which the function is increasing and (f) The
For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = -x3 + 8x2 + 63; k = 4
For each polynomial function, one zero is given. Find all other zeros.ƒ(x) = 4x3 + 6x2 - 2x - 1; 1/2
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = (4x + 3)(x + 2)2
Graph each quadratic function. Give the (a) Vertex, (b) Axis, (c) Domain, (d) Range. Then determine (e) The largest open interval of the domain over which the function is increasing (f) The
For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = 2x2 - 3x - 3; k = 2
For each polynomial function, one zero is given. Find all other zeros.ƒ(x) = x3 - 7x2 + 17x - 15; 2 - i
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = (3x - 1)(x + 2)2
Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. Then determine (e) the largest open interval of the domain over which the function is increasing and ( f ) the
For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = x2 - 4x - 5; k = 5

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