Solve x^3 2x^2-x-1,0

Question

Simplify the expression

2 x^{5} - x - 1

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} - x - 1

Show Solution

(x - 1) (2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} - x - 1

Calculate

2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + x - 2 x^{4} - 2 x^{3} - 2 x^{2} - 2 x - 1

Rewrite the expression

x \times 2 x^{4} + x \times 2 x^{3} + x \times 2 x^{2} + x \times 2 x + x - 2 x^{4} - 2 x^{3} - 2 x^{2} - 2 x - 1

Factor out x from the expression

x (2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1) - 2 x^{4} - 2 x^{3} - 2 x^{2} - 2 x - 1

Factor out - 1 from the expression

x (2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1) - (2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1)

Solution

(x - 1) (2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1)

Show Solution

x = 1

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} - x - 1 = 0

Factor the expression

(x - 1) (2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1) = 0

Separate the equation into 2 possible cases

x - 1 = 0 2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1 = 0

Solve the equation

x = 1 x \in / R

Solution

x = 1

Show Solution