Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x³−11x²+7x−5;f(4)

In Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=x²+6x+3

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. f(x)=x³+2x²+5x+4

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x³−x−1; between 1 and 2

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. h(x)=(x+7)/(x²+4x−21)

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x³−4x²+2; between 0 and 1

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (1−x)²(x−5/2)<0

Use the Rational Zero Theorem to list all possible rational zeros for each given function. $f\left(x\right)=x^4-6x^3+14x^2-14x+5$

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=3x³−7x²−2x+5;f(−3)

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.f(x)=2x⁴−4x²+1; between -1 and 0

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. r(x)=(x²+4x−21)/(x+7)

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $x^3+2x^2-x-2\ge 0$

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. f(x)=5x³−3x²+3x−1

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2x²+4x−3

In Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x⁴+6x³−18x²; between 2 and 3

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $x^3+2x^2-4x-8\ge 0$

In Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2x−x²−2

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation.

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x³+x²−2x+1; between -3 and -2

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. $f\left(x\right)=3x^4-2x^3-8x+5$

Find the horizontal asymptote, if there is one, of the graph of each rational function. f(x)=12x/(3x²+1)

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. f(x)=2x⁴−5x³−x²−6x+4

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=x⁴+5x³+5x²−5x−6;f(3)

In Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x⁵−x³−1; between 1 and 2

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $x^3+x^2+4x+4>0$

Find all zeros of the polynomial function or solve the given polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root. f(x)=x³−4x²−7x+10

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=3x³−10x+9; between -3 and -2

An equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=3x²−12x−1

Find the horizontal asymptote, if there is one, of the graph of each rational function. g(x)=12x²/(3x²+1)

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x⁴−5x³−x²+3x+2; f(−1/2)