Solve x^5 - 4 x^4 - 3 x^3 2 x^2 - x

Question

Simplify the expression

- 5 x^{5} - 4 x^{4} - x

Evaluate

x^{5} - 4 x^{4} - 3 x^{3} \times 2 x^{2} - x

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

- 6 x^{3 + 2}

Add the numbers

- 6 x^{5}

x^{5} - 4 x^{4} - 6 x^{5} - x

Solution

More Steps

Evaluate

x^{5} - 6 x^{5}

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

(1 - 6) x^{5}

Subtract the numbers

- 5 x^{5}

- 5 x^{5} - 4 x^{4} - x

Show Solution

Factor the expression

- x (5 x^{4} + 4 x^{3} + 1)

Evaluate

x^{5} - 4 x^{4} - 3 x^{3} \times 2 x^{2} - x

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

6 x^{3 + 2}

Add the numbers

6 x^{5}

x^{5} - 4 x^{4} - 6 x^{5} - x

Subtract the terms

More Steps

Simplify

x^{5} - 4 x^{4} - 6 x^{5}

Subtract the terms

More Steps

Evaluate

x^{5} - 6 x^{5}

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

(1 - 6) x^{5}

Subtract the numbers

- 5 x^{5}

- 5 x^{5} - 4 x^{4}

- 5 x^{5} - 4 x^{4} - x

Rewrite the expression

- x \times 5 x^{4} - x \times 4 x^{3} - x

Solution

- x (5 x^{4} + 4 x^{3} + 1)

Show Solution

Find the roots

x = 0

Evaluate

x^{5} - 4 x^{4} - 3 x^{3} \times 2 x^{2} - x

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

x^{5} - 4 x^{4} - 3 x^{3} \times 2 x^{2} - x = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

6 x^{3 + 2}

Add the numbers

6 x^{5}

x^{5} - 4 x^{4} - 6 x^{5} - x = 0

Subtract the terms

More Steps

Simplify

x^{5} - 4 x^{4} - 6 x^{5}

Subtract the terms

More Steps

Evaluate

x^{5} - 6 x^{5}

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

(1 - 6) x^{5}

Subtract the numbers

- 5 x^{5}

- 5 x^{5} - 4 x^{4}

- 5 x^{5} - 4 x^{4} - x = 0

Factor the expression

- x (5 x^{4} + 4 x^{3} + 1) = 0

Divide both sides

x (5 x^{4} + 4 x^{3} + 1) = 0

Separate the equation into 2 possible cases

x = 0 5 x^{4} + 4 x^{3} + 1 = 0

Solve the equation

x = 0 x \in / R

Solution

x = 0

Show Solution