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Questions and Answers of College Algebra

For each polynomial function, one zero is given. Find all other zeros.ƒ(x) = x3 + 4x2 - 5; 1
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = x2(x - 5)(x + 3)(x - 1)
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 + 5x + 6; k = -2
For each polynomial function, one zero is given. Find all other zeros.ƒ(x) = x3 - x2 - 4x - 6; 3
Factor ƒ(x) into linear factors given that k is a zero.ƒ(x) = 2x4 + x3 - 9x2 - 13x - 5; k = -1 (multiplicity 3)
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = x(x + 1)(x - 1)
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
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) = 3x4 + 4x3 - 10x2 + 15; k = -1
Factor ƒ(x) into linear factors given that k is a zero.ƒ(x) = x4 + 2x3 - 7x2 - 20x - 12; k = -2 (multiplicity 2)
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = 2x(x - 3)(x + 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
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) = 2x4 + x3 - 15x2 + 3x; k = -3
Factor ƒ(x) into linear factors given that k is a zero.ƒ(x) = 6x3 + (19 - 6i)x2 + (16 - 7i)x + (4 - 2i); k = -2 + i
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = x3 + 3x2 - 13x - 15
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
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) = 4x4 - 3x3 - 20x2 - x; k = 3
Factor ƒ(x) into linear factors given that k is a zero.ƒ(x) = 2x3 + (3 - 2i)x2 + (-8 - 5i)x + (3 + 3i); k = 1 + i
If ƒ(x) is a polynomial function with real coefficients, and if 7 + 2i is a zero of the function, then what other complex number must also be a zero?
Use synthetic division to determine whether k is a zero of the function.ƒ(x) = 2x3 + 5x2 + 30; k = -4
Use synthetic division to determine whether k is a zero of the function.ƒ(x) = x3 + 2x2 + 3x + 2; k = -1
Use synthetic division to find ƒ(2).ƒ(x) = 2x3 + 5x2 + 30; k = -4
Use synthetic division to find ƒ(2).ƒ(x) = 5x4 - 12x2 + 2x - 8
Use synthetic division to find ƒ(2).ƒ(x) = 2x3 - 3x2 + 7x - 12
Use synthetic division to find ƒ(2).ƒ(x) = -x3 + 5x2 - 7x + 1
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) = -3x3 + 5x - 6; k = -1
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) = 5x3 - 3x2 + 2x - 6; k = 2
Use synthetic division to perform each division. |Зx3 + 6х2 — 8х + 3 х+ 3
Use synthetic division to perform each division. 2х3 - х + 6 x + 6
Use synthetic division to perform each division. 3x3 + 8x? + 5x + 10 x + 2
Use synthetic division to perform each division. х3 + x2 — 11х — 10 х — 3
Use the answer to Exercise 14 and the graph of ƒ to solve the following. Give approximations to the nearest hundredth.(a) ƒ(x) > 0 (b) ƒ(x) < 0
Graph the function in the standard viewing window of a calculator, and use the calculator to solve the equation ƒ(x) = 0. Express solutions as approximations to the nearest hundredth.
Use the discriminant to explain how to determine the number of x-intercepts the graph of ƒ(x) will have before graphing it on a calculator.
In 1990, the International Panel on Climate Change (IPCC) stated that if current trends of burning fossil fuel and deforestation were to continue, then future amounts of atmospheric carbon dioxide in
During the course of a year, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x) = 2x2 - 32x + 150 between the months of January and August. Here x is time
A projectile is fired vertically upward, and its height s(t) in feet after t seconds is given by the function s(t) = -16t2 + 800t + 600.(a) From what height was the projectile fired?(b) After how
Use a quadratic function to find the dimensions of the rectangular region of maximum area that can be enclosed with 180 m of fencing, if no fencing is needed along one side of the region.
Consider the functionIf a is positive, what is the least value of ax2 + bx + c in terms of a, b, and c?
Consider the functionUnder what conditions will its graph have one or more x-intercepts? For these conditions, express the x-intercept(s) in terms of a, h, and k.
Consider the functionWhat are the coordinates of the lowest point of its graph?
Consider the functionƒ(x) = a(x - h)2 + k, for a > 0.
Graph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing.ƒ(x) =
Graph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing.ƒ(x) =
Graph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing. f(x) :
Graph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing.ƒ(x) =
Variation occurs in a formula from photography. Inthe luminance, L, varies directly as the square of the F-stop, F, and inversely as the product of the film ASA number, s, and the shutter speed,
A measure of malnutrition, called the pelidisi, varies directly as the cube root of a person’s weight in grams and inversely as the person’s sitting height in centimeters. A person with a
Suppose the effects of detonating a nuclear bomb will be felt over a distance from the point of detonation that is directly proportional to the cube root of the yield of the bomb. Suppose a
The Stefan-Boltzmann law says that the radiation of heat R from an object is directly proportional to the fourth power of the kelvin temperature of the object. For a certain object, R = 213.73 at
According to Poiseuille’s law, the resistance to flow of a blood vessel, R, is directly proportional to the length, l, and inversely proportional to the fourth power of the radius, r. If R = 25
The roof of a new sports arena rests on round concrete pillars. The maximum load a cylindrical column of circular cross section can hold varies directly as the fourth power of the diameter and
Solve each problemThe volume of a right circular cylinder is jointly proportional to the square of the radius of the circular base and to the height. If the volume is 300 cm3 when the height is 10.62
Solve each problemThe force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. If a wind of 40 mph exerts a force of 50 lb on a
Solve each problemThe volume of a gas varies inversely as the pressure and directly as the temperature in kelvins (K). If a certain gas occupies a volume of 1.3 L at 300 K and a pressure of 18
Solve each problemSimple interest varies jointly as principal and time. If $1000 invested for 2 yr earned $70, find the amount of interest earned by $5000 for 5 yr.
Solve the problemThe illumination produced by a light source varies inversely as the square of the distance from the source. The illumination of a light source at 5 m is 70 candelas. What is the
Solve each problemIn electric current flow, it is found that the resistance offered by a fixed length of wire of a given material varies inversely as the square of the diameter of the wire. If a wire
Solve each problemThe weight of an object varies inversely as the square of its distance from the center of Earth. If an object 8000 mi from the center of Earth weighs 90 lb, find its weight when it
Solve each problemThe speed of a pulley varies inversely as its diameter. One kind of pulley, with diameter 3 in., turns at 150 revolutions per minute. Find the speed of a similar pulley with
Solve each problemThe current in a simple electrical circuit varies inversely as the resistance. If the current is 50 amps when the resistance is 10 ohms, find the current if the resistance is 5 ohms.
Solve each problemHooke’s law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 15 lb stretches a certain spring 8 in., how much
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. 1 (x) = -(x 2) + 4 2
Solve each problemThe amount of water emptied by a pipe varies directly as the square of the diameter of the pipe. For a certain constant water flow, a pipe emptying into a canal will allow 200 gal
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.2x4 + 5x3 - 2x2 + 5x + 6; x + 3
Solve each problemThe distance that a person can see to the horizon on a clear day from a point above the surface of Earth varies directly as the square root of the height at that point. If a person
Use synthetic division to perform each division. x4 — Зх3 — 4х? + 12х х — 2
Solve each problemThe weight of an object on Earth is directly proportional to the weight of that same object on the moon. A 200-lb astronaut would weigh 32 lb on the moon. How much would a 50-lb dog
Graph the following on the same coordinate system.(a) y = x2 (b) y = 3x2 (c) y = 1/3 x2(d) How does the coefficient of x2 affect the shape of the graph?
Solve each problemThe resistance in ohms of a platinum wire temperature sensor varies directly as the temperature in kelvins (K). If the resistance is 646 ohms at a temperature of 190 K, find the
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. f(x) =(x+ 1)3 – 3
Solve each problemThe pressure exerted by a certain liquid at a given point varies directly as the depth of the point beneath the surface of the liquid. The pressure at 10 ft is 50 pounds per square
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.5x4 + 16x3 - 15x2 + 8x + 16; x + 4
Solve each problemThe circumference of a circle varies directly as the radius. A circle with radius 7 in. has circumference 43.96 in. Find the circumference of the circle if the radius changes to 11
Write each formula as an English phrase using the word varies or proportional.ƒ = mv2/r, where ƒ is the centripetal force of an object of mass m moving along a circle of radius r at velocity v
For the polynomial functions in Exercises that have irrational zeros, find approximations to the nearest thousandth.
Write each formula as an English phrase using the word varies or proportional.s = kx3, where s is the strength of a muscle that has length x
Use synthetic division to perform each division. x4 — х3 — 5х? — 3x 5x2 х+1
Write each formula as an English phrase using the word varies or proportional.d = 1/4πnr2, where d is the distance a gas atom of radius r travels between collisions, and n is the number of atoms per
Factor ƒ(x) into linear factors given that k is a zero.ƒ(x) = 2x3 - 3x2 - 17x + 30; k = 2
Use synthetic division to perform each division. х3 — 1 х — 1
Graph the following on the same coordinate system.(a) y = (x - 2)2 (b) y = (x + 1)2 (c) y = (x + 3)2(d) How do these graphs differ from the graph of y = x2?
Write each formula as an English phrase using the word varies or proportional.C = 2πr, where C is the circumference of a circle of radius r
Match each statement with its corresponding graph in choices A–D. In each case, k > 0.x varies directly as the second powerof y. (x = ky2) А. У В. У C. y D. — х х х х
Match each statement with its corresponding graph in choices A–D. In each case, k > 0.y varies directly as the second power of x. (y = kx2) А. У В. У C. y D. — х х х х
Write each formula as an English phrase using the word varies or proportional.d = 1/5 s, where d is the approximate distance (in miles) from a storm, and s is the number of seconds between seeing
A quadratic function ƒ(x) has vertex (0, 0), and all of its intercepts are the same point. What is the general form of its equation?
Match each statement with its corresponding graph in choices A–D. In each case, k > 0.y varies directly as x. (y = kx) А. У В. У C. y D. — х х х х
Use an end behavior diagramto describe the end behavior of the graph of each polynomial function.ƒ(x) = -4x3 + 3x2 - 1 or
Solve each problem.Let y vary directly as x, and inversely as m2 and r2. If y = 5/3 when x = 1, m = 2, and r = 3, find y when x = 3, m = 1, and r = 8.
Factor ƒ(x) into linear factors given that k is a zero.ƒ(x) = 6x3 + 13x2 - 14x + 3; k = -3
Write each formula as an English phrase using the word varies or proportional.r = d/t, where r is the speed when traveling d miles in t hours
Use synthetic division to perform each division. x5 + 1 х+1
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
Solve each problem.Let a be directly proportional to m and n2, and inversely proportional to y3. If a = 9 when m = 4, n = 9, and y = 3, find a when m = 6, n = 2, and y = 5.
Use an end behavior diagramto describe the end behavior of the graph of each polynomial function.ƒ(x) = 4x7 - x5 + x3 - 1 or
Solve each problem.Suppose p varies directly as the square of z, and inversely as r. If p = 32/5 when z = 4 and r = 10, find p when z = 3 and r = 32.
Solve each problem.Suppose r varies directly as the square of m, and inversely as s. If r = 12 when m = 6 and s = 4, find r when m = 6 and s = 20.
Fill in the blank(s) to correctly complete each sentence, or answer the question as appropriate.Consider the two ordered pairs (x, y) from Exercise 4. Multiply the y-value by the x-value. What is the
Fill in the blank(s) to correctly complete each sentence, or answer the question as appropriate.Consider the two ordered pairs (x, y) from Exercise 3. Divide the y-value by the x-value. What is the

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