Solve for x.

\displaystyle x(x +2)(x - 5) = 0

Solve for x.

\displaystyle (x - 1)(x - 4)(x + 3) = 0

Solve for x.

\displaystyle (3x + 2)(x + 9)( x - 2) = 0

Solve for x.

\displaystyle (x - 7)(3x + 2)(x + 1) = 0

Solve for x.

\displaystyle (4x - 1)(2x - 3)(x + 8) = 0

Solve for x.

\displaystyle (2x - 5)(2x + 5)(x - 7) = 0

Solve for x.

\displaystyle (5x - 8)(x + 3)(2x - 1) = 0

Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.

Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.

Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.

Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.

Use the graph to determine the roots of the corresponding polynomial equation. The roots are all integral values.

Determine the real roots of each polynomial equation.

(x^2 +1)(x - 4) = 0

Determine the real roots of each polynomial equation.

(x^2- 1)(x^2 + 4) = 0

Determine the real roots of each polynomial equation.

(3x^2 + 27)(x^2 - 16) = 0

Determine the real roots of each polynomial equation.

(x^4 - 1)(x^2 - 25) = 0

Determine the real roots of each polynomial equation.

(4x^2 - 9)(x^2 + 16) = 0

Determine the real roots of each polynomial equation.

(x^2 + 7x + 12)(x^2 - 49) = 0

Determine the real roots of each polynomial equation.

(2x^2 + 5x - 3)(4x^2 - 100) = 0

Determine the x-intercepts of the graph of each polynomial function.

y = x^3 - 4x^2 - 45x

Determine the x-intercepts of the graph of each polynomial function.

y = x^4 - 81x^2

Determine the x-intercepts of the graph of each polynomial function.

y = 6x^3 - 5x^2 - 4x

Determine the x-intercepts of the graph of each polynomial function.

y = x^3 + x^2 - 4x - 4

Determine the x-intercepts of the graph of each polynomial function.

y = x^4 - 16

Determine the x-intercepts of the graph of each polynomial function.

y = x^4- 2x^3 - x^2 + 2x

Determine the x-intercepts of the graph of each polynomial function.

y = x^4 - 29x^2 + 100

Is this statement true or false? If the statement is false, reword it to make it true.

• If the graph of a quartic function has two x-intercepts, then the corresponding quartic equation has four real roots.

Is this statement true or false? If the statement is false, reword it to make it true.

• All the roots of a polynomial equation correspond to the x-int of the graph of the corresponding polynomial function.

Is this statement true or false? If the statement is false, reword it to make it true.

• A polynomial equation of degree three must have at least one real root.

Is this statement true or false? If the statement is false, reword it to make it true.

• All polynomial equations can be solved algebraically.

Is this statement true or false? If the statement is false, reword it to make it true.

• All polynomial equations can be solved graphically.

Solve by factoring.

x^3 - 4x^2 - 3x + 18 = 0

Solve by factoring.

x^3 - 4x^2 - 7x + 10 = 0

Solve by factoring.

x^3 - 5x^2 + 7x - 3 = 0

Solve by factoring.

x^3 + x^2 - 8x - 12 = 0

Solve by factoring.

x^3 - 3x^2 - 4x + 12 = 0

Solve by factoring.

x^3 + 2x^2 - 7x + 4 = 0

Solve by factoring.

x^3 - 3x^2 + x + 5 = 0

Solve by factoring.

2x^3 + 3x^2 - 5x - 6 = 0

Solve by factoring.

2x^3 - 11x^2 + 12x + 9 = 0

Solve by factoring.

9x^3 + 18x^2 - 4x - 8 = 0

Solve by factoring.

5x^3 - 8x^2 - 27x + 18 = 0

Solve by factoring.

8x^4 - 64x= 0

Solve by factoring.

4x^4 - 2x^3 - 16x^2 + 8x = 0

Solve by factoring.

x^4 - x^3 - 11x^2 + 9x + 18 = 0

Solve by factoring.

x^3 - 5x^2 + 8 = -2x

Solve by factoring.

x^3 - x^2 = 4x + 6

Solve by factoring.

2x^3 - 7x^2 + 10x - 5 = 0

Solve by factoring.

x^4 - x^3 = 2x + 4

Solve by factoring.

x^4 + 13x^3 = -36

The width of a square based storage tank is 3 m less than its height. The tank has a capacity of 20 m^3. If the dimensions are integer values in metres, what are they?

The passenger section of a train has width 2x - 7, length 2x +3, and height x - 2, with all dimensions in metres. Solve a polynomial equation to determine the dimensions of the section of the train if the volume is 117 m^3.

Is it possible for a polynomial equation to have exactly one irrational root?

Is it possible for a polynomial equation to have exactly one non-real root?

The distance, d, in kilometres, travelled by a plane after t hours can be represented by d(t) = -4t^3 + 40t^2 + 500t, where 0 \leq t \leq 10. How long does the plane take to fly 4088 km?

A steel beam is supported by two vertical walls. When a 1000-kg weight is placed on the beam, x metres from one end, the vertical deflection, d, in metres, can be calculated using the formula d(x) = 0.0005(x^4-16x^3 + 512x). How far from the end of the beam should the weight be placed for a deflection of 0 m?

Based on research, the marketing team at Best of U predicts that when the price of a bottle of a new SPF 50 sunscreen is x dollars, the number, D, in hundreds, of bottles sold per month can be modelled by the function D(x) =-x^3 + 8x^2 + 9x + 100

• Graph the function D(x). Write the domain for this situation.

Based on research, the marketing team at Best of U predicts that when the price of a bottle of a new SPF 50 sunscreen is x dollars, the number, D, in hundreds, of bottles sold per month can be modelled by the function D(x) =-x^3 + 8x^2 + 9x + 100

• How many bottles are sold per month when the price of each bottle is $5?

Based on research, the marketing team at Best of U predicts that when the price of a bottle of a new SPF 50 sunscreen is x dollars, the number, D, in hundreds, of bottles sold per month can be modelled by the function D(x) =-x^3 + 8x^2 + 9x + 100

• Determine the value(s) of x that will result in sales of 17 200 bottles of sunscreen per month.
  

Solve. Round answers to one decimal place if necessary.

2(x - 1)^3 = 16

Solve. Round answers to one decimal place if necessary.

2(x^2 - 4x)^2 - 5(x^2 - 4x) = 3

Determine the value of k such that -2 is one root of the equation 2x^3 + (k + 1)x^2 = 4- x^2

(a) Determine the value of k such that -2 is one root of the equation 2x^3 + (k + 1)x^2 = 4- x^2

(b) Determine the other roots of the equation. Justify your answer.

Open-top boxes are constructed by cutting equal squares from the corners of cardboard sheet that measure 32 cm by 28 cm. Determine possible dimensions of the boxes if each has a volume of 1920 cm^3.

A complex number is a number that can be written in the form a + bi, where a and b are real numbers and i = \sqrt{-1}. When the quadratic formula is used and the discriminant is negative, complex numbers result.

(a) Find all the real and complex solutions to x^3 - 27 = 0

(b) Determine a polynomial equation of degree three with roots x = 3 \pm i and x = -4. Is this equation unique? Explain.

The dimensions of a gift box are consecutive positive integers such that the height is the least integer and the length is the greatest integer. If the height is increased by 1 cm, the width is increased by 2 cm, and the length is increased by 3 cm, then a larger box is constructed such that the volume is increased by 456 cm^3. Determine the dimensions of each box.

The roots of the equation 6x^3 + 17x^2 - 5x - 6 = 0 are represented by a, b, and c (from least to greatest). Determine an equation whose roots are a + b, \frac{a}{b}, and ab.

Determine the product of all values of k for which the polynomial equation 2x^3 - 9x^2 + 12 x - k = 0 has a double root.