Solve (x^2-x-6) * (x-2)

Question

Simplify the expression

x^{3} - 3 x^{2} - 4 x + 12

Evaluate

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

Apply the distributive property

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

Multiply the terms

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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 2 - x \times x - (- x \times 2) - 6 x - (- 6 \times 2)

Use the commutative property to reorder the terms

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the numbers

x^{3} - 2 x^{2} - x^{2} - (- 2 x) - 6 x - (- 12)

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} - 2 x^{2} - x^{2} + 2 x - 6 x + 12

Subtract the terms

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Evaluate

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

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

(- 2 - 1) x^{2}

Subtract the numbers

- 3 x^{2}

x^{3} - 3 x^{2} + 2 x - 6 x + 12

Solution

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Evaluate

2 x - 6 x

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

(2 - 6) x

Subtract the numbers

- 4 x

x^{3} - 3 x^{2} - 4 x + 12

Show Solution

Factor the expression

(x - 3) (x + 2) (x - 2)

Evaluate

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

Solution

More Steps

Evaluate

x^{2} - x - 6

Rewrite the expression

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

Calculate

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

Rewrite the expression

x \times x + x \times 2 - 3 x - 3 \times 2

Factor out x from the expression

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

Factor out - 3 from the expression

x (x + 2) - 3 (x + 2)

Factor out x + 2 from the expression

(x - 3) (x + 2)

(x - 3) (x + 2) (x - 2)

Show Solution

Find the roots

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

Evaluate

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

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

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

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

x^{2} - x - 6 = 0

Factor the expression

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Evaluate

x^{2} - x - 6

Rewrite the expression

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

Calculate

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

Rewrite the expression

x \times x + x \times 2 - 3 x - 3 \times 2

Factor out x from the expression

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

Factor out - 3 from the expression

x (x + 2) - 3 (x + 2)

Factor out x + 2 from the expression

(x - 3) (x + 2)

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

When the product of factors equals 0,at least one factor is 0

x - 3 = 0 x + 2 = 0

Solve the equation for x

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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 = 3 x + 2 = 0

Solve the equation for x

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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 = 3 x = - 2

x = 3 x = - 2 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 = 3 x = - 2 x = 2

Solution

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

Show Solution