Exam 4: Polynomial and Rational Functions

Provide an appropriate response. -What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

(Multiple Choice)

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Question 361

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $- 7 x ^ { 3 } + 32 x ^ { 2 } - 14 x + 5 ; x + 5$

(Multiple Choice)

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Question 362

Round to the nearest tenth unless indicated otherwise. -The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the car's speed, and inversely as the radius of the curve. If a force of 3600 pounds is Needed to keep an 1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet, What force would be required to keep the same car from skidding on a curve of radius 590 feet at 60 mph? Round your answer to the nearest pound of force.

(Multiple Choice)

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Question 363

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x\left(x^{2}-9\right)(x+1)^{3}$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x\left(x^{2}-9\right)(x+1)^{3}$

(Multiple Choice)

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Question 364

Solve the problem -The area of a square is numerically 5 more than the perimeter. Find the length of the side.

(Multiple Choice)

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Question 365

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$ -intercept?

(Multiple Choice)

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Question 366

Round to the nearest tenth unless indicated otherwise. -At a fixed temperature, the resistance R of a wire varies directly as the length l and inversely as the square of its diameter d. If the resistance is 0.48 ohm when the diameter is 1 mm and the length is 240 cm, what is the resistance when the diameter is 3 mm and the length is 430 cm?

(Multiple Choice)

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Question 367

Find a polynomial function f(x) of least possible degree having the graph shown. -

(Multiple Choice)

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Question 368

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12$

(Multiple Choice)

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Question 369

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } - 7$

(Multiple Choice)

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Question 370

Find a polynomial function f(x) of least possible degree having the graph shown. -

(Multiple Choice)

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Question 371

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 64$

(Multiple Choice)

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Question 372

Identify the vertex of the parabola. - $y = - 2 x ^ { 2 } - 12 x - 23$

(Multiple Choice)

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Question 373

Translate the given formula to an English phrase using the word "varies". -If s varies directly as t2, and s = 567 when t = 9, find s when t is 4.

(Multiple Choice)

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Question 374

Provide an appropriate response. -A quadratic equation f(x) = 0 has a solution x = 3. Its graph has vertex (-1, -16). What is the other solution of the equation?

(Multiple Choice)

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Question 375

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 3 ) ^ { 2 } - 1$

(Multiple Choice)

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Question 376

Translate the given formula to an English phrase using the word "varies". - $\mathrm { y }$ varies directly as the square of $\mathrm { z }$ and $\mathrm { y } = 384$ when $\mathrm { z } = 8$ . Find $\mathrm { y }$ when $\mathrm { z }$ is 9 .

(Multiple Choice)

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Question 377

Solve the problem -A can has a surface area of 926 square inches. Its height is $7.35$ inches. What is the radius of the circular top? Round to the nearest hundredth.

(Multiple Choice)

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Question 378

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 3 x ^ { 4 } - 9 x ^ { 3 } + 2 x ^ { 2 } - 6 x ; k = 3$

(Multiple Choice)

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Question 379

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 81 } { x - 3 }$

(Multiple Choice)

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Question 380

Showing 361 - 380 of 508

Provide an appropriate response. -What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $- 7 x ^ { 3 } + 32 x ^ { 2 } - 14 x + 5 ; x + 5$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x\left(x^{2}-9\right)(x+1)^{3}$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x\left(x^{2}-9\right)(x+1)^{3}$

Solve the problem -The area of a square is numerically 5 more than the perimeter. Find the length of the side.

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$ -intercept?

Find a polynomial function f(x) of least possible degree having the graph shown. -

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } - 7$

Find a polynomial function f(x) of least possible degree having the graph shown. -

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 64$

Identify the vertex of the parabola. - $y = - 2 x ^ { 2 } - 12 x - 23$

Translate the given formula to an English phrase using the word "varies". -If s varies directly as t2, and s = 567 when t = 9, find s when t is 4.

Provide an appropriate response. -A quadratic equation f(x) = 0 has a solution x = 3. Its graph has vertex (-1, -16). What is the other solution of the equation?

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 3 ) ^ { 2 } - 1$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { y }$ varies directly as the square of $\mathrm { z }$ and $\mathrm { y } = 384$ when $\mathrm { z } = 8$ . Find $\mathrm { y }$ when $\mathrm { z }$ is 9 .

Solve the problem -A can has a surface area of 926 square inches. Its height is $7.35$ inches. What is the radius of the circular top? Round to the nearest hundredth.

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 3 x ^ { 4 } - 9 x ^ { 3 } + 2 x ^ { 2 } - 6 x ; k = 3$

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 81 } { x - 3 }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

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Exam 4: Polynomial and Rational Functions

Provide an appropriate response. -What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - −7x3+32x2−14x+5;x+5- 7 x ^ { 3 } + 32 x ^ { 2 } - 14 x + 5 ; x + 5−7x3+32x2−14x+5;x+5

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x(x2−9)(x+1)3f(x)=x\left(x^{2}-9\right)(x+1)^{3}f(x)=x(x2−9)(x+1)3

Solve the problem -The area of a square is numerically 5 more than the perimeter. Find the length of the side.

Provide an appropriate response. -For what value of ccc does the quadratic function f(x)=x2−6x+cf ( x ) = x ^ { 2 } - 6 x + cf(x)=x2−6x+c have exactly one xxx -intercept?

Find a polynomial function f(x) of least possible degree having the graph shown. -

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x3+4x2−10x+12f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12f(x)=x3+4x2−10x+12

Find the equation of the axis of symmetry of the parabola. - f(x)=x2−7f ( x ) = x ^ { 2 } - 7f(x)=x2−7

Find a polynomial function f(x) of least possible degree having the graph shown. -

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x3−64f ( x ) = x ^ { 3 } - 64f(x)=x3−64

Identify the vertex of the parabola. - y=−2x2−12x−23y = - 2 x ^ { 2 } - 12 x - 23y=−2x2−12x−23

Translate the given formula to an English phrase using the word "varies". -If s varies directly as t2, and s = 567 when t = 9, find s when t is 4.

Provide an appropriate response. -A quadratic equation f(x) = 0 has a solution x = 3. Its graph has vertex (-1, -16). What is the other solution of the equation?

Find the equation of the axis of symmetry of the parabola. - f(x)=(x+3)2−1f ( x ) = ( x + 3 ) ^ { 2 } - 1f(x)=(x+3)2−1

Translate the given formula to an English phrase using the word "varies". - y\mathrm { y }y varies directly as the square of z\mathrm { z }z and y=384\mathrm { y } = 384y=384 when z=8\mathrm { z } = 8z=8 . Find y\mathrm { y }y when z\mathrm { z }z is 9 .

Solve the problem -A can has a surface area of 926 square inches. Its height is 7.357.357.35 inches. What is the radius of the circular top? Round to the nearest hundredth.

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=3x4−9x3+2x2−6x;k=3f ( x ) = 3 x ^ { 4 } - 9 x ^ { 3 } + 2 x ^ { 2 } - 6 x ; k = 3f(x)=3x4−9x3+2x2−6x;k=3

Use synthetic division to perform the division. - x4+81x−3\frac { x ^ { 4 } + 81 } { x - 3 }x−3x4+81​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $- 7 x ^ { 3 } + 32 x ^ { 2 } - 14 x + 5 ; x + 5$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x\left(x^{2}-9\right)(x+1)^{3}$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x\left(x^{2}-9\right)(x+1)^{3}$

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$ -intercept?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } - 7$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 64$

Identify the vertex of the parabola. - $y = - 2 x ^ { 2 } - 12 x - 23$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 3 ) ^ { 2 } - 1$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { y }$ varies directly as the square of $\mathrm { z }$ and $\mathrm { y } = 384$ when $\mathrm { z } = 8$ . Find $\mathrm { y }$ when $\mathrm { z }$ is 9 .

Solve the problem -A can has a surface area of 926 square inches. Its height is $7.35$ inches. What is the radius of the circular top? Round to the nearest hundredth.

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 3 x ^ { 4 } - 9 x ^ { 3 } + 2 x ^ { 2 } - 6 x ; k = 3$

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 81 } { x - 3 }$