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

Question

Simplify the expression

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

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

10 x^{3 + 2}

Add the numbers

10 x^{5}

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

Show Solution

x^{4} (10 x - 1)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

10 x^{3 + 2}

Add the numbers

10 x^{5}

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

Rewrite the expression

x^{4} \times 10 x - x^{4}

Solution

x^{4} (10 x - 1)

Show Solution

x_{1} = 0, x_{2} = \frac{1}{10}

Alternative Form

x_{1} = 0, x_{2} = 0.1

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

10 x^{3 + 2}

Add the numbers

10 x^{5}

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

Factor the expression

x^{4} (10 x - 1) = 0

Separate the equation into 2 possible cases

x^{4} = 0 10 x - 1 = 0

The only way a power can be 0 is when the base equals 0

x = 0 10 x - 1 = 0

Solve the equation

More Steps

Evaluate

10 x - 1 = 0

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

10 x = 0 + 1

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

10 x = 1

Divide both sides

\frac{10 x}{10} = \frac{1}{10}

Divide the numbers

x = \frac{1}{10}

x = 0 x = \frac{1}{10}

Solution

x_{1} = 0, x_{2} = \frac{1}{10}

Alternative Form

x_{1} = 0, x_{2} = 0.1

Show Solution