Solve (x^3)(x^2-2x-8)

Question

Simplify the expression

x^{5} - 2 x^{4} - 8 x^{3}

Evaluate

x^{3} (x^{2} - 2 x - 8)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

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

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 2}

Add the numbers

x^{5}

x^{5} - x^{3} \times 2 x - x^{3} \times 8

Multiply the terms

More Steps

Evaluate

x^{3} \times 2 x

Use the commutative property to reorder the terms

2 x^{3} \times x

Multiply the terms

More Steps

Evaluate

x^{3} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 1}

Add the numbers

x^{4}

2 x^{4}

x^{5} - 2 x^{4} - x^{3} \times 8

Solution

x^{5} - 2 x^{4} - 8 x^{3}

Show Solution

Factor the expression

x^{3} (x - 4) (x + 2)

Evaluate

x^{3} (x^{2} - 2 x - 8)

Solution

More Steps

Evaluate

x^{2} - 2 x - 8

Rewrite the expression

x^{2} + (2 - 4) x - 8

Calculate

x^{2} + 2 x - 4 x - 8

Rewrite the expression

x \times x + x \times 2 - 4 x - 4 \times 2

Factor out x from the expression

x (x + 2) - 4 x - 4 \times 2

Factor out - 4 from the expression

x (x + 2) - 4 (x + 2)

Factor out x + 2 from the expression

(x - 4) (x + 2)

x^{3} (x - 4) (x + 2)

Show Solution

Find the roots

x_{1} = - 2, x_{2} = 0, x_{3} = 4

Evaluate

(x^{3}) (x^{2} - 2 x - 8)

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

(x^{3}) (x^{2} - 2 x - 8) = 0

Calculate

x^{3} (x^{2} - 2 x - 8) = 0

Separate the equation into 2 possible cases

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

The only way a power can be 0 is when the base equals 0

x = 0 x^{2} - 2 x - 8 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 2 x - 8 = 0

Factor the expression

More Steps

Evaluate

x^{2} - 2 x - 8

Rewrite the expression

x^{2} + (2 - 4) x - 8

Calculate

x^{2} + 2 x - 4 x - 8

Rewrite the expression

x \times x + x \times 2 - 4 x - 4 \times 2

Factor out x from the expression

x (x + 2) - 4 x - 4 \times 2

Factor out - 4 from the expression

x (x + 2) - 4 (x + 2)

Factor out x + 2 from the expression

(x - 4) (x + 2)

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

When the product of factors equals 0,at least one factor is 0

x - 4 = 0 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 4 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = 4 x = - 2

x = 0 x = 4 x = - 2

Solution

x_{1} = - 2, x_{2} = 0, x_{3} = 4

Show Solution