Solve x^3 3x^2-2x

Question

Simplify the expression

3 x^{5} - 2 x

Evaluate

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

Solution

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} - 2 x

Show Solution

Factor the expression

x (3 x^{4} - 2)

Evaluate

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

Multiply

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} - 2 x

Rewrite the expression

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

Solution

x (3 x^{4} - 2)

Show Solution

Find the roots

x_{1} = - \frac{4 54}{3}, x_{2} = 0, x_{3} = \frac{4 54}{3}

Alternative Form

x_{1} \approx - 0.903602, x_{2} = 0, x_{3} \approx 0.903602

Evaluate

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

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

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

Factor the expression

x (3 x^{4} - 2) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{4} - 2 = 0

Solve the equation

More Steps

Evaluate

3 x^{4} - 2 = 0

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

3 x^{4} = 0 + 2

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

3 x^{4} = 2

Divide both sides

\frac{3 x ^{4}}{3} = \frac{2}{3}

Divide the numbers

x^{4} = \frac{2}{3}

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

x = \pm 4 \frac{2}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 2}{4 3}

Multiply by the Conjugate

\frac{4 2 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 2 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

\frac{4 54}{4 3 \times 4 3 ^{3}}

Multiply the numbers

\frac{4 54}{3}

x = \pm \frac{4 54}{3}

Separate the equation into 2 possible cases

x = \frac{4 54}{3} x = - \frac{4 54}{3}

x = 0 x = \frac{4 54}{3} x = - \frac{4 54}{3}

Solution

x_{1} = - \frac{4 54}{3}, x_{2} = 0, x_{3} = \frac{4 54}{3}

Alternative Form

x_{1} \approx - 0.903602, x_{2} = 0, x_{3} \approx 0.903602

Show Solution