Solve (x - 2)(x - 5)(x 1)

Question

Simplify the expression

x^{3} - 7 x^{2} + 10 x

Evaluate

(x - 2) (x - 5) (x \times 1)

Remove the parentheses

(x - 2) (x - 5) x \times 1

Any expression multiplied by 1 remains the same

(x - 2) (x - 5) x

Multiply the terms

More Steps

Evaluate

(x - 2) (x - 5)

Apply the distributive property

x \times x - x \times 5 - 2 x - (- 2 \times 5)

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the numbers

x^{2} - 5 x - 2 x - (- 10)

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} - 5 x - 2 x + 10

Subtract the terms

More Steps

Evaluate

- 5 x - 2 x

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

(- 5 - 2) x

Subtract the numbers

- 7 x

x^{2} - 7 x + 10

(x^{2} - 7 x + 10) x

Apply the distributive property

x^{2} \times x - 7 x \times x + 10 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}

x^{3} - 7 x \times x + 10 x

Solution

x^{3} - 7 x^{2} + 10 x

Show Solution

Find the roots

x_{1} = 0, x_{2} = 2, x_{3} = 5

Evaluate

(x - 2) (x - 5) (x \times 1)

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

(x - 2) (x - 5) (x \times 1) = 0

Any expression multiplied by 1 remains the same

(x - 2) (x - 5) x = 0

Separate the equation into 3 possible cases

x - 2 = 0 x - 5 = 0 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 = 2 x - 5 = 0 x = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 2 x = 5 x = 0

Solution

x_{1} = 0, x_{2} = 2, x_{3} = 5

Show Solution