Solve x^3 3x^2-4x-1

Question

Simplify the expression

3 x^{5} - 4 x - 1

Evaluate

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

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} - 4 x - 1

Show Solution

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

Evaluate

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

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} - 4 x - 1

Calculate

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

Rewrite the expression

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

Factor out x from the expression

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

Solution

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

Show Solution

x_{1} = - 1, x_{2} \approx - 0.250743, x_{3} \approx 1.129643

Evaluate

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

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

x^{3} \times 3 x^{2} - 4 x - 1 = 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} - 4 x - 1 = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

Solve the equation

x = - 1 x \approx 1.129643 x \approx - 0.250743

Solution

x_{1} = - 1, x_{2} \approx - 0.250743, x_{3} \approx 1.129643

Show Solution