Solve x^3 2x^2 - 8x

Question

Simplify the expression

2 x^{5} - 8 x

Evaluate

x^{3} \times 2 x^{2} - 8 x

Solution

More Steps

Evaluate

x^{3} \times 2 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} - 8 x

Show Solution

2 x (x^{2} - 2) (x^{2} + 2)

Evaluate

x^{3} \times 2 x^{2} - 8 x

Evaluate

More Steps

Evaluate

x^{3} \times 2 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} - 8 x

Factor out 2 x from the expression

2 x (x^{4} - 4)

Solution

More Steps

Evaluate

x^{4} - 4

Rewrite the expression in exponential form

(x^{2})^{2} - 2^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(x^{2} - 2) (x^{2} + 2)

2 x (x^{2} - 2) (x^{2} + 2)

Show Solution

x_{1} = - 2, x_{2} = 0, x_{3} = 2

Alternative Form

x_{1} \approx - 1.414214, x_{2} = 0, x_{3} \approx 1.414214

Evaluate

x^{3} \times 2 x^{2} - 8 x

To find the roots of the expression,set the expression equal to 0

x^{3} \times 2 x^{2} - 8 x = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 2 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} - 8 x = 0

Factor the expression

2 x (x^{4} - 4) = 0

Divide both sides

x (x^{4} - 4) = 0

Separate the equation into 2 possible cases

x = 0 x^{4} - 4 = 0

Solve the equation

More Steps

Evaluate

x^{4} - 4 = 0

Move the constant to the right-hand side and change its sign

x^{4} = 0 + 4

Removing 0 doesn't change the value,so remove it from the expression

x^{4} = 4

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 44

Simplify the expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

x = \pm 2

Separate the equation into 2 possible cases

x = 2 x = - 2

x = 0 x = 2 x = - 2

Solution

x_{1} = - 2, x_{2} = 0, x_{3} = 2

Alternative Form

x_{1} \approx - 1.414214, x_{2} = 0, x_{3} \approx 1.414214

Show Solution