Solve (x-1)(x-2)(x-3)

Question

Simplify the expression

x^{3} - 6 x^{2} + 11 x - 6

Evaluate

(x - 1) (x - 2) (x - 3)

Multiply the terms

More Steps

Evaluate

(x - 1) (x - 2)

Apply the distributive property

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

Multiply the terms

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

Use the commutative property to reorder the terms

x^{2} - 2 x - 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

x^{2} - 2 x - x + 2

Subtract the terms

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Evaluate

- 2 x - x

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

(- 2 - 1) x

Subtract the numbers

- 3 x

x^{2} - 3 x + 2

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

Apply the distributive property

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

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Multiply the numbers

x^{3} - 3 x^{2} - 3 x^{2} - (- 9 x) + 2 x - 2 \times 3

Multiply the numbers

x^{3} - 3 x^{2} - 3 x^{2} - (- 9 x) + 2 x - 6

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^{3} - 3 x^{2} - 3 x^{2} + 9 x + 2 x - 6

Subtract the terms

More Steps

Evaluate

- 3 x^{2} - 3 x^{2}

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

(- 3 - 3) x^{2}

Subtract the numbers

- 6 x^{2}

x^{3} - 6 x^{2} + 9 x + 2 x - 6

Solution

More Steps

Evaluate

9 x + 2 x

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

(9 + 2) x

Add the numbers

11 x

x^{3} - 6 x^{2} + 11 x - 6

Show Solution

Find the roots

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

Evaluate

(x - 1) (x - 2) (x - 3)

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

(x - 1) (x - 2) (x - 3) = 0

Separate the equation into 3 possible cases

x - 1 = 0 x - 2 = 0 x - 3 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 x - 2 = 0 x - 3 = 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 = 1 x = 2 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 = 1 x = 2 x = 3

Solution

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

Show Solution