Solve (x - 2 ) ( x^23 x - 1 )

Question

Simplify the expression

3 x^{4} - x - 6 x^{3} + 2

Evaluate

(x - 2) (x^{2} \times 3 x - 1)

Multiply

More Steps

Evaluate

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

(x - 2) (3 x^{3} - 1)

Apply the distributive property

x \times 3 x^{3} - x \times 1 - 2 \times 3 x^{3} - (- 2 \times 1)

Multiply the terms

More Steps

Evaluate

x \times 3 x^{3}

Use the commutative property to reorder the terms

3 x \times x^{3}

Multiply the terms

More Steps

Evaluate

x \times x^{3}

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

x^{1 + 3}

Add the numbers

x^{4}

3 x^{4}

3 x^{4} - x \times 1 - 2 \times 3 x^{3} - (- 2 \times 1)

Any expression multiplied by 1 remains the same

3 x^{4} - x - 2 \times 3 x^{3} - (- 2 \times 1)

Multiply the numbers

3 x^{4} - x - 6 x^{3} - (- 2 \times 1)

Any expression multiplied by 1 remains the same

3 x^{4} - x - 6 x^{3} - (- 2)

Solution

3 x^{4} - x - 6 x^{3} + 2

Show Solution

Find the roots

x_{1} = \frac{3 9}{3}, x_{2} = 2

Alternative Form

x_{1} \approx 0.693361, x_{2} = 2

Evaluate

(x - 2) (x^{2} \times 3 x - 1)

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

(x - 2) (x^{2} \times 3 x - 1) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

(x - 2) (3 x^{3} - 1) = 0

Separate the equation into 2 possible cases

x - 2 = 0 3 x^{3} - 1 = 0

Solve the equation

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 = 2 3 x^{3} - 1 = 0

Solve the equation

More Steps

Evaluate

3 x^{3} - 1 = 0

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

3 x^{3} = 0 + 1

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

3 x^{3} = 1

Divide both sides

\frac{3 x ^{3}}{3} = \frac{1}{3}

Divide the numbers

x^{3} = \frac{1}{3}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{3}

Calculate

x = 3 \frac{1}{3}

Simplify the root

More Steps

Evaluate

3 \frac{1}{3}

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

\frac{3 1}{3 3}

Simplify the radical expression

\frac{1}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

\frac{3 9}{3}

x = \frac{3 9}{3}

x = 2 x = \frac{3 9}{3}

Solution

x_{1} = \frac{3 9}{3}, x_{2} = 2

Alternative Form

x_{1} \approx 0.693361, x_{2} = 2

Show Solution