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

Question

Simplify the expression

3 x^{4} - 12 x^{3} + 9 x^{2}

Evaluate

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

Multiply the terms

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

Multiply the terms

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Evaluate

3 x^{2} (x - 3)

Apply the distributive property

3 x^{2} \times x - 3 x^{2} \times 3

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}

3 x^{3} - 3 x^{2} \times 3

Multiply the numbers

3 x^{3} - 9 x^{2}

(3 x^{3} - 9 x^{2}) (x - 1)

Apply the distributive property

3 x^{3} \times x - 3 x^{3} \times 1 - 9 x^{2} \times x - (- 9 x^{2} \times 1)

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}

3 x^{4} - 3 x^{3} \times 1 - 9 x^{2} \times x - (- 9 x^{2} \times 1)

Any expression multiplied by 1 remains the same

3 x^{4} - 3 x^{3} - 9 x^{2} \times x - (- 9 x^{2} \times 1)

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}

3 x^{4} - 3 x^{3} - 9 x^{3} - (- 9 x^{2} \times 1)

Any expression multiplied by 1 remains the same

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

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

Solution

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Evaluate

- 3 x^{3} - 9 x^{3}

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

(- 3 - 9) x^{3}

Subtract the numbers

- 12 x^{3}

3 x^{4} - 12 x^{3} + 9 x^{2}

Show Solution

Find the roots

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

Evaluate

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

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

3 (x - 3) (x - 1) (x^{2}) = 0

Calculate

3 (x - 3) (x - 1) x^{2} = 0

Multiply the terms

3 x^{2} (x - 3) (x - 1) = 0

Elimination the left coefficient

x^{2} (x - 3) (x - 1) = 0

Separate the equation into 3 possible cases

x^{2} = 0 x - 3 = 0 x - 1 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x - 3 = 0 x - 1 = 0

Solve the equation

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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 = 0 x = 3 x - 1 = 0

Solve the equation

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Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 0 x = 3 x = 1

Solution

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

Show Solution