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

Question

Simplify the expression

x^{4} - 6 x^{3} + 11 x^{2} - 6 x

Evaluate

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

Multiply the terms

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

Multiply the terms

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

Apply the distributive property

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the terms

More Steps

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

Multiply the numbers

x^{4} - 3 x^{3} - 3 x^{3} - (- 9 x^{2}) + 2 x \times x - 2 x \times 3

Multiply the terms

x^{4} - 3 x^{3} - 3 x^{3} - (- 9 x^{2}) + 2 x^{2} - 2 x \times 3

Multiply the numbers

x^{4} - 3 x^{3} - 3 x^{3} - (- 9 x^{2}) + 2 x^{2} - 6 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^{4} - 3 x^{3} - 3 x^{3} + 9 x^{2} + 2 x^{2} - 6 x

Subtract the terms

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x^{4} - 6 x^{3} + 9 x^{2} + 2 x^{2} - 6 x

Solution

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x^{4} - 6 x^{3} + 11 x^{2} - 6 x

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Find the roots

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

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