Solve x^5 - x^(2) 3x^2

Question

Simplify the expression

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

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 3

Add the numbers

x^{4} \times 3

Use the commutative property to reorder the terms

3 x^{4}

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

Show Solution

x^{4} (x - 3)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 3

Add the numbers

x^{4} \times 3

Use the commutative property to reorder the terms

3 x^{4}

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

Rewrite the expression

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

Solution

x^{4} (x - 3)

Show Solution

x_{1} = 0, x_{2} = 3

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 3

Add the numbers

x^{4} \times 3

Use the commutative property to reorder the terms

3 x^{4}

x^{5} - 3 x^{4} = 0

Factor the expression

x^{4} (x - 3) = 0

Separate the equation into 2 possible cases

x^{4} = 0 x - 3 = 0

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

x = 0 x - 3 = 0

Solve the equation

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 0 x = 3

Solution

x_{1} = 0, x_{2} = 3

Show Solution