Solve x^32x-x^5 - ScanMath

Question

Simplify the expression

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

Evaluate

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

Solution

More Steps

Evaluate

x^{3} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{3 + 1} \times 2

Add the numbers

x^{4} \times 2

Use the commutative property to reorder the terms

2 x^{4}

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

Show Solution

x^{4} (2 - x)

Evaluate

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

Multiply

More Steps

Evaluate

x^{3} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{3 + 1} \times 2

Add the numbers

x^{4} \times 2

Use the commutative property to reorder the terms

2 x^{4}

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

Rewrite the expression

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

Solution

x^{4} (2 - x)

Show Solution

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

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

x^{3} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{3 + 1} \times 2

Add the numbers

x^{4} \times 2

Use the commutative property to reorder the terms

2 x^{4}

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

Factor the expression

x^{4} (2 - x) = 0

Separate the equation into 2 possible cases

x^{4} = 0 2 - x = 0

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

x = 0 2 - x = 0

Solve the equation

More Steps

Evaluate

2 - x = 0

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

- x = 0 - 2

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

- x = - 2

Change the signs on both sides of the equation

x = 2

x = 0 x = 2

Solution

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

Show Solution