Solve (x-2)(x-3)(x-4)

Question

(x - 2) (x - 3) (x - 4)

Simplify the expression

x^{3} - 9 x^{2} + 26 x - 24

Evaluate

(x - 2) (x - 3) (x - 4)

Multiply the terms

More Steps

Evaluate

(x - 2) (x - 3)

Apply the distributive property

x \times x - x \times 3 - 2 x - (- 2 \times 3)

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the numbers

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

Subtract the terms

More Steps

Evaluate

- 3 x - 2 x

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

(- 3 - 2) x

Subtract the numbers

- 5 x

x^{2} - 5 x + 6

(x^{2} - 5 x + 6) (x - 4)

Apply the distributive property

x^{2} \times x - x^{2} \times 4 - 5 x \times x - (- 5 x \times 4) + 6 x - 6 \times 4

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 4 - 5 x \times x - (- 5 x \times 4) + 6 x - 6 \times 4

Use the commutative property to reorder the terms

x^{3} - 4 x^{2} - 5 x \times x - (- 5 x \times 4) + 6 x - 6 \times 4

Multiply the terms

x^{3} - 4 x^{2} - 5 x^{2} - (- 5 x \times 4) + 6 x - 6 \times 4

Multiply the numbers

x^{3} - 4 x^{2} - 5 x^{2} - (- 20 x) + 6 x - 6 \times 4

Multiply the numbers

x^{3} - 4 x^{2} - 5 x^{2} - (- 20 x) + 6 x - 24

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} - 4 x^{2} - 5 x^{2} + 20 x + 6 x - 24

Subtract the terms

More Steps

Evaluate

- 4 x^{2} - 5 x^{2}

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

(- 4 - 5) x^{2}

Subtract the numbers

- 9 x^{2}

x^{3} - 9 x^{2} + 20 x + 6 x - 24

Solution

More Steps

Evaluate

20 x + 6 x

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

(20 + 6) x

Add the numbers

26 x

x^{3} - 9 x^{2} + 26 x - 24

Show Solution

Find the roots

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

Evaluate

(x - 2) (x - 3) (x - 4)

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

(x - 2) (x - 3) (x - 4) = 0

Separate the equation into 3 possible cases

x - 2 = 0 x - 3 = 0 x - 4 = 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 - 3 = 0 x - 4 = 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 = 2 x = 3 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 = 2 x = 3 x = 4

Solution

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

Show Solution