Solve ((x^5)(x 1)(x-2))/4

Question

Simplify the expression

\frac{x ^{7} - 2 x ^{6}}{4}

Evaluate

\frac{x ^{5} ( x \times 1 ) ( x - 2 )}{4}

Remove the parentheses

\frac{x ^{5} \times x \times 1 \times ( x - 2 )}{4}

Multiply the terms

More Steps

Evaluate

x^{5} \times x \times 1 \times (x - 2)

Rewrite the expression

x^{5} \times x (x - 2)

Multiply the terms with the same base by adding their exponents

x^{5 + 1} (x - 2)

Add the numbers

x^{6} (x - 2)

\frac{x ^{6} ( x - 2 )}{4}

Solution

More Steps

Evaluate

x^{6} (x - 2)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x^{6} \times x

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

x^{6 + 1}

Add the numbers

x^{7}

x^{7} - x^{6} \times 2

Use the commutative property to reorder the terms

x^{7} - 2 x^{6}

\frac{x ^{7} - 2 x ^{6}}{4}

Show Solution

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

Evaluate

\frac{( x ^{5} ) ( x \times 1 ) ( x - 2 )}{4}

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

\frac{( x ^{5} ) ( x \times 1 ) ( x - 2 )}{4} = 0

Calculate

\frac{x ^{5} ( x \times 1 ) ( x - 2 )}{4} = 0

Any expression multiplied by 1 remains the same

\frac{x ^{5} \times x ( x - 2 )}{4} = 0

Multiply

More Steps

Multiply the terms

x^{5} \times x (x - 2)

Multiply the terms with the same base by adding their exponents

x^{5 + 1} (x - 2)

Add the numbers

x^{6} (x - 2)

\frac{x ^{6} ( x - 2 )}{4} = 0

Simplify

x^{6} (x - 2) = 0

Separate the equation into 2 possible cases

x^{6} = 0 x - 2 = 0

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

x = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 2 = 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

x = 0 x = 2

Solution

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

Show Solution