Solve -(1 x)(x-2)(4-x)> _0

Question

Simplify the expression

- 6 x^{2} + x^{3} + 8 x

Evaluate

- (1 \times x) (x - 2) (4 - x)

Remove the parentheses

- 1 \times x (x - 2) (4 - x)

Any expression multiplied by 1 remains the same

- x (x - 2) (4 - x)

Multiply the terms

More Steps

Evaluate

- x (x - 2)

Apply the distributive property

- x \times x - (- x \times 2)

Multiply the terms

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

Use the commutative property to reorder the terms

- x^{2} - (- 2 x)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- x^{2} + 2 x

(- x^{2} + 2 x) (4 - x)

Apply the distributive property

- x^{2} \times 4 - (- x^{2} \times x) + 2 x \times 4 - 2 x \times x

Use the commutative property to reorder the terms

- 4 x^{2} - (- x^{2} \times x) + 2 x \times 4 - 2 x \times x

Multiply the terms

More Steps

Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

- 4 x^{2} - (- x^{3}) + 2 x \times 4 - 2 x \times x

Multiply the numbers

- 4 x^{2} - (- x^{3}) + 8 x - 2 x \times x

Multiply the terms

- 4 x^{2} - (- x^{3}) + 8 x - 2 x^{2}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 4 x^{2} + x^{3} + 8 x - 2 x^{2}

Solution

More Steps

Evaluate

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

Collect like terms by calculating the sum or difference of their coefficients

(- 4 - 2) x^{2}

Subtract the numbers

- 6 x^{2}

- 6 x^{2} + x^{3} + 8 x

Show Solution

Find the roots

x_{1} = 0, x_{2} = 2, x_{3} = 4

Evaluate

- (1 \times x) (x - 2) (4 - x)

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

- (1 \times x) (x - 2) (4 - x) = 0

Any expression multiplied by 1 remains the same

- x (x - 2) (4 - x) = 0

Change the sign

x (x - 2) (4 - x) = 0

Separate the equation into 3 possible cases

x = 0 x - 2 = 0 4 - x = 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 4 - x = 0

Solve the equation

More Steps

Evaluate

4 - x = 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

Change the signs on both sides of the equation

x = 4

x = 0 x = 2 x = 4

Solution

x_{1} = 0, x_{2} = 2, x_{3} = 4

Show Solution