Factor ƒ(x) into linear factors given that k is a zero. $\text{ƒ}\left(x\right)=-6x^3-25x^2-3x+4;k=-4$

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=9x⁶-3x⁴+x²-2

Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. (2x - 1)(5x - 9)(x - 4) < 0

Write each formula as an English phrase using the word varies or proportional. V = 1/3 πr²h, where V is the volume of a cone of radius r and height h

Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given. √3, -√3, 2, 3

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = (x - 5)² - 4

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=10x⁶-x⁵+2x-2

Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given. -2+√5, -2-√5, -2, 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) = 2x³ + 3x² - 16x+10; k = -4

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = -(1/2)(x + 1)² - 3

Circumference of a Circle The 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 in.

Solve each polynomial inequality. Give the solution set in interval notation. (x - 4)(2x + 3)(3x - 1) ≥ 0

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=3+2x-4x²-5x¹⁰

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=7+2x-5x²-10x⁴

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = -3 (x - 2)² +1

Solve each polynomial inequality. Give the solution set in interval notation. (x - 3)(x - 4)(x - 5)² ≤ 0

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once.

$\text{ƒ}\left(x\right)=\frac{(x+7)}{(x+1)}$

Resistance of a Wire The 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 resistance at a temperature of 250 K.

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = x² + 6x + 5

Find all rational zeros of each function. $\text{ƒ}\left(x\right)=8x^4-14x^3-29x^2-4x+3$

Distance to the Horizon The 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 144 m above the surface of Earth can see 18 km to the horizon, how far can a person see to the horizon from a point 64 m above the surface?

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. ƒ(x)=1/(x+4)

Factor $\text{ƒ}\left(x\right)$ into linear factors given that k is a zero. $\text{ƒ}\left(x\right)=x^4+2x^3-7x^2-20x-12;k=-2$ (multiplicity $2$)

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=-2x(x-3)(x+2)

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

Solve each polynomial inequality. Give the solution set in interval notation. -(x - 3)(x - 4)² (x - 5) > 0

Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=3x^3-8x^2+x+2 between -1 and 0

Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=3x^3-8x^2+x+2 between 2 and 3

Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=3x^3-8x^2+x+2 Find the zero in part (b) to three decimal places.

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=-x(x+1)(x-1)