Solve x^3 3x^2-6x 18

Question

Simplify the expression

3 x^{5} - 108 x

Evaluate

x^{3} \times 3 x^{2} - 6 x \times 18

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 3

Add the numbers

x^{5} \times 3

Use the commutative property to reorder the terms

3 x^{5}

3 x^{5} - 6 x \times 18

Solution

3 x^{5} - 108 x

Show Solution

3 x (x^{2} - 6) (x^{2} + 6)

Evaluate

x^{3} \times 3 x^{2} - 6 x \times 18

Evaluate

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 3

Add the numbers

x^{5} \times 3

Use the commutative property to reorder the terms

3 x^{5}

3 x^{5} - 6 x \times 18

Evaluate

3 x^{5} - 108 x

Factor out 3 x from the expression

3 x (x^{4} - 36)

Solution

More Steps

Evaluate

x^{4} - 36

Rewrite the expression in exponential form

(x^{2})^{2} - 6^{2}

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

(x^{2} - 6) (x^{2} + 6)

3 x (x^{2} - 6) (x^{2} + 6)

Show Solution

x_{1} = - 6, x_{2} = 0, x_{3} = 6

Alternative Form

x_{1} \approx - 2.44949, x_{2} = 0, x_{3} \approx 2.44949

Evaluate

x^{3} \times 3 x^{2} - 6 x \times 18

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

x^{3} \times 3 x^{2} - 6 x \times 18 = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 3

Add the numbers

x^{5} \times 3

Use the commutative property to reorder the terms

3 x^{5}

3 x^{5} - 6 x \times 18 = 0

Multiply the terms

3 x^{5} - 108 x = 0

Factor the expression

3 x (x^{4} - 36) = 0

Divide both sides

x (x^{4} - 36) = 0

Separate the equation into 2 possible cases

x = 0 x^{4} - 36 = 0

Solve the equation

More Steps

Evaluate

x^{4} - 36 = 0

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

x^{4} = 0 + 36

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

x^{4} = 36

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

x = \pm 436

Simplify the expression

x = \pm 6

Separate the equation into 2 possible cases

x = 6 x = - 6

x = 0 x = 6 x = - 6

Solution

x_{1} = - 6, x_{2} = 0, x_{3} = 6

Alternative Form

x_{1} \approx - 2.44949, x_{2} = 0, x_{3} \approx 2.44949

Show Solution