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

Question

Simplify the expression

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

Evaluate

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

Multiply the first two terms

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

Multiply the terms

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Evaluate

x^{2} (x - 3)

Apply the distributive property

x^{2} \times x - 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}

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

Use the commutative property to reorder the terms

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

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

Apply the distributive property

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

Multiply the terms

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Evaluate

x^{3} \times 2 x

Use the commutative property to reorder the terms

2 x^{3} \times x

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}

2 x^{4}

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

Use the commutative property to reorder the terms

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

Multiply the terms

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Evaluate

- 3 x^{2} \times 2 x

Multiply the numbers

- 6 x^{2} \times x

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}

- 6 x^{3}

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

Multiply the numbers

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

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

Solution

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Evaluate

- 3 x^{3} - 6 x^{3}

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

(- 3 - 6) x^{3}

Subtract the numbers

- 9 x^{3}

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

Show Solution

Find the roots

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

Alternative Form

x_{1} = 0, x_{2} = 1.5, x_{3} = 3

Evaluate

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

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

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

Calculate

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

Multiply the first two terms

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

Separate the equation into 3 possible cases

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

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

x = 0 x - 3 = 0 2 x - 3 = 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 2 x - 3 = 0

Solve the equation

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Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

\frac{2 x}{2} = \frac{3}{2}

Divide the numbers

x = \frac{3}{2}

x = 0 x = 3 x = \frac{3}{2}

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 1.5, x_{3} = 3

Show Solution