Solve (x^(4)-x^(3)-x^(2))(x^(2)-2x 1)

Question

Simplify the expression

x^{6} - 3 x^{5} + x^{4} + 2 x^{3}

Evaluate

(x^{4} - x^{3} - x^{2}) (x^{2} - 2 x \times 1)

Multiply the terms

(x^{4} - x^{3} - x^{2}) (x^{2} - 2 x)

Apply the distributive property

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

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

Multiply the terms

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

Multiply the terms

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

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^{6} - 2 x^{5} - x^{5} + 2 x^{4} - x^{4} + 2 x^{3}

Subtract the terms

More Steps

x^{6} - 3 x^{5} + 2 x^{4} - x^{4} + 2 x^{3}

Solution

More Steps

x^{6} - 3 x^{5} + x^{4} + 2 x^{3}

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Factor the expression

x^{3} (x^{2} - x - 1) (x - 2)

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Find the roots

x_{1} = \frac{1 - 5}{2}, x_{2} = 0, x_{3} = \frac{1 + 5}{2}, x_{4} = 2

Alternative Form

x_{1} \approx - 0.618034, x_{2} = 0, x_{3} \approx 1.618034, x_{4} = 2

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