Solve (x-4)(x^4)(x 1)

Question

Simplify the expression

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

Evaluate

(x - 4) x^{4} (x \times 1)

Remove the parentheses

(x - 4) x^{4} \times x \times 1

Rewrite the expression

(x - 4) x^{4} \times x

Multiply the terms with the same base by adding their exponents

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

Add the numbers

(x - 4) x^{5}

Multiply the terms

x^{5} (x - 4)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x^{5} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{5 + 1}

Add the numbers

x^{6}

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

Solution

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

Show Solution

x_{1} = 0, x_{2} = 4

Evaluate

(x - 4) (x^{4}) (x \times 1)

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

(x - 4) (x^{4}) (x \times 1) = 0

Calculate

(x - 4) x^{4} (x \times 1) = 0

Any expression multiplied by 1 remains the same

(x - 4) x^{4} \times x = 0

Multiply the terms

More Steps

Multiply the terms

(x - 4) x^{4} \times x

Multiply the terms with the same base by adding their exponents

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

Add the numbers

(x - 4) x^{5}

Multiply the terms

x^{5} (x - 4)

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

Separate the equation into 2 possible cases

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

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

x = 0 x - 4 = 0

Solve the equation

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 0 x = 4

Solution

x_{1} = 0, x_{2} = 4

Show Solution