Solve x(x-1)(x-3)(x-7)/10

Question

x (x - 1) (x - 3) \times \frac{x - 7}{10}

Simplify the expression

\frac{x ^{4} - 11 x ^{3} + 31 x ^{2} - 21 x}{10}

Evaluate

x (x - 1) (x - 3) \times \frac{x - 7}{10}

Multiply the terms

\frac{x ( x - 7 )}{10} (x - 1) (x - 3)

Multiply the first two terms

\frac{x ( x - 7 ) ( x - 1 )}{10} (x - 3)

Multiply the terms

\frac{x ( x - 7 ) ( x - 1 ) ( x - 3 )}{10}

Solution

More Steps

Evaluate

x (x - 7) (x - 1) (x - 3)

Multiply the terms

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(x^{2} - 7 x) (x - 1) (x - 3)

Multiply the terms

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(x^{3} - 8 x^{2} + 7 x) (x - 3)

Apply the distributive property

x^{3} \times x - x^{3} \times 3 - 8 x^{2} \times x - (- 8 x^{2} \times 3) + 7 x \times x - 7 x \times 3

Multiply the terms

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x^{4} - x^{3} \times 3 - 8 x^{2} \times x - (- 8 x^{2} \times 3) + 7 x \times x - 7 x \times 3

Use the commutative property to reorder the terms

x^{4} - 3 x^{3} - 8 x^{2} \times x - (- 8 x^{2} \times 3) + 7 x \times x - 7 x \times 3

Multiply the terms

More Steps

x^{4} - 3 x^{3} - 8 x^{3} - (- 8 x^{2} \times 3) + 7 x \times x - 7 x \times 3

Multiply the numbers

x^{4} - 3 x^{3} - 8 x^{3} - (- 24 x^{2}) + 7 x \times x - 7 x \times 3

Multiply the terms

x^{4} - 3 x^{3} - 8 x^{3} - (- 24 x^{2}) + 7 x^{2} - 7 x \times 3

Multiply the numbers

x^{4} - 3 x^{3} - 8 x^{3} - (- 24 x^{2}) + 7 x^{2} - 21 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} - 8 x^{3} + 24 x^{2} + 7 x^{2} - 21 x

Subtract the terms

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x^{4} - 11 x^{3} + 24 x^{2} + 7 x^{2} - 21 x

Add the terms

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x^{4} - 11 x^{3} + 31 x^{2} - 21 x

\frac{x ^{4} - 11 x ^{3} + 31 x ^{2} - 21 x}{10}

Show Solution

Find the roots

x_{1} = 0, x_{2} = 1, x_{3} = 3, x_{4} = 7

Show Solution