Solve (x^2-36)(x 1)(x-2)

Question

Simplify the expression

x^{4} - 2 x^{3} - 36 x^{2} + 72 x

Evaluate

(x^{2} - 36) (x \times 1) (x - 2)

Remove the parentheses

(x^{2} - 36) x \times 1 \times (x - 2)

Any expression multiplied by 1 remains the same

(x^{2} - 36) x (x - 2)

Multiply the first two terms

x (x^{2} - 36) (x - 2)

Multiply the terms

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Evaluate

x (x^{2} - 36)

Apply the distributive property

x \times x^{2} - x \times 36

Multiply the terms

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Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

x^{3} - x \times 36

Use the commutative property to reorder the terms

x^{3} - 36 x

(x^{3} - 36 x) (x - 2)

Apply the distributive property

x^{3} \times x - x^{3} \times 2 - 36 x \times x - (- 36 x \times 2)

Multiply the terms

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Evaluate

x^{3} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 1}

Add the numbers

x^{4}

x^{4} - x^{3} \times 2 - 36 x \times x - (- 36 x \times 2)

Use the commutative property to reorder the terms

x^{4} - 2 x^{3} - 36 x \times x - (- 36 x \times 2)

Multiply the terms

x^{4} - 2 x^{3} - 36 x^{2} - (- 36 x \times 2)

Multiply the numbers

x^{4} - 2 x^{3} - 36 x^{2} - (- 72 x)

Solution

x^{4} - 2 x^{3} - 36 x^{2} + 72 x

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Factor the expression

x (x - 6) (x + 6) (x - 2)

Evaluate

(x^{2} - 36) (x \times 1) (x - 2)

Remove the parentheses

(x^{2} - 36) x \times 1 \times (x - 2)

Any expression multiplied by 1 remains the same

(x^{2} - 36) x (x - 2)

Multiply the first two terms

x (x^{2} - 36) (x - 2)

Solution

x (x - 6) (x + 6) (x - 2)

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Find the roots

x_{1} = - 6, x_{2} = 0, x_{3} = 2, x_{4} = 6

Evaluate

(x^{2} - 36) (x \times 1) (x - 2)

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

(x^{2} - 36) (x \times 1) (x - 2) = 0

Any expression multiplied by 1 remains the same

(x^{2} - 36) x (x - 2) = 0

Multiply the first two terms

x (x^{2} - 36) (x - 2) = 0

Separate the equation into 3 possible cases

x = 0 x^{2} - 36 = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 36 = 0

Move the constant to the right-hand side and change its sign

x^{2} = 0 + 36

Removing 0 doesn't change the value,so remove it from the expression

x^{2} = 36

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 36

Simplify the expression

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Evaluate

36

Write the number in exponential form with the base of 6

6^{2}

Reduce the index of the radical and exponent with 2

6

x = \pm 6

Separate the equation into 2 possible cases

x = 6 x = - 6

x = 0 x = 6 x = - 6 x - 2 = 0

Solve the equation

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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 = 0 x = 6 x = - 6 x = 2

Solution

x_{1} = - 6, x_{2} = 0, x_{3} = 2, x_{4} = 6

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