Solve x^(3)-x^(2) 2x-1

Question

Simplify the expression

- x^{3} - 1

Evaluate

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

Multiply

More Steps

Multiply the terms

- x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 2

Add the numbers

- x^{3} \times 2

Use the commutative property to reorder the terms

- 2 x^{3}

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

Solution

More Steps

Evaluate

x^{3} - 2 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 2) x^{3}

Subtract the numbers

- x^{3}

- x^{3} - 1

Show Solution

Factor the expression

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

Evaluate

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

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

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

Subtract the terms

More Steps

Simplify

x^{3} - 2 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 2) x^{3}

Subtract the numbers

- x^{3}

- x^{3} - 1

Factor out - 1 from the expression

- (x^{3} + 1)

Solution

More Steps

Evaluate

x^{3} + 1

Calculate

x^{3} - x^{2} + x + x^{2} - x + 1

Rewrite the expression

x \times x^{2} - x \times x + x + x^{2} - x + 1

Factor out x from the expression

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

Factor out x^{2} - x + 1 from the expression

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

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

Show Solution

Find the roots

x = - 1

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

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

Subtract the terms

More Steps

Simplify

x^{3} - 2 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 2) x^{3}

Subtract the numbers

- x^{3}

- x^{3} - 1 = 0

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

- x^{3} = 0 + 1

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

- x^{3} = 1

Change the signs on both sides of the equation

x^{3} = - 1

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

3 x^{3} = 3 - 1

Calculate

x = 3 - 1

Solution

More Steps

Evaluate

3 - 1

An odd root of a negative radicand is always a negative

- 31

Simplify the radical expression

- 1

x = - 1

Show Solution