Solve (3x-1)(3x^2 -5x-2)

Вопрос

Simplify the expression

Solution

9 x^{3} - 18 x^{2} - x + 2

Evaluate

(3 x - 1) (3 x^{2} - 5 x - 2)

Apply the distributive property

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

Multiply the terms

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Evaluate

3 x \times 3 x^{2}

Multiply the numbers

9 x \times x^{2}

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}

9 x^{3}

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

Multiply the terms

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Evaluate

3 x \times 5 x

Multiply the numbers

15 x \times x

Multiply the terms

15 x^{2}

9 x^{3} - 15 x^{2} - 3 x \times 2 - 3 x^{2} - (- 5 x) - (- 2)

Multiply the numbers

9 x^{3} - 15 x^{2} - 6 x - 3 x^{2} - (- 5 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

9 x^{3} - 15 x^{2} - 6 x - 3 x^{2} + 5 x + 2

Subtract the terms

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Evaluate

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

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

(- 15 - 3) x^{2}

Subtract the numbers

- 18 x^{2}

9 x^{3} - 18 x^{2} - 6 x + 5 x + 2

Решение

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Evaluate

- 6 x + 5 x

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

(- 6 + 5) x

Add the numbers

- x

9 x^{3} - 18 x^{2} - x + 2

Показать решение

Factor the expression

Factor

(3 x - 1) (x - 2) (3 x + 1)

Evaluate

(3 x - 1) (3 x^{2} - 5 x - 2)

Решение

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Evaluate

3 x^{2} - 5 x - 2

Rewrite the expression

3 x^{2} + (1 - 6) x - 2

Calculate

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

Rewrite the expression

x \times 3 x + x - 2 \times 3 x - 2

Factor out x from the expression

x (3 x + 1) - 2 \times 3 x - 2

Factor out - 2 from the expression

x (3 x + 1) - 2 (3 x + 1)

Factor out 3 x + 1 from the expression

(x - 2) (3 x + 1)

(3 x - 1) (x - 2) (3 x + 1)

Показать решение

Find the roots

Find the roots of the algebra expression

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0. \dot{3}, x_{3} = 2

Evaluate

(3 x - 1) (3 x^{2} - 5 x - 2)

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

(3 x - 1) (3 x^{2} - 5 x - 2) = 0

Separate the equation into 2 possible cases

3 x - 1 = 0 3 x^{2} - 5 x - 2 = 0

Solve the equation

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Evaluate

3 x - 1 = 0

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

3 x = 0 + 1

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

3 x = 1

Divide both sides

\frac{3 x}{3} = \frac{1}{3}

Divide the numbers

x = \frac{1}{3}

x = \frac{1}{3} 3 x^{2} - 5 x - 2 = 0

Solve the equation

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Evaluate

3 x^{2} - 5 x - 2 = 0

Factor the expression

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Evaluate

3 x^{2} - 5 x - 2

Rewrite the expression

3 x^{2} + (1 - 6) x - 2

Calculate

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

Rewrite the expression

x \times 3 x + x - 2 \times 3 x - 2

Factor out x from the expression

x (3 x + 1) - 2 \times 3 x - 2

Factor out - 2 from the expression

x (3 x + 1) - 2 (3 x + 1)

Factor out 3 x + 1 from the expression

(x - 2) (3 x + 1)

(x - 2) (3 x + 1) = 0

When the product of factors equals 0,at least one factor is 0

x - 2 = 0 3 x + 1 = 0

Solve the equation for x

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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 = 2 3 x + 1 = 0

Solve the equation for x

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Evaluate

3 x + 1 = 0

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

3 x = 0 - 1

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

3 x = - 1

Divide both sides

\frac{3 x}{3} = \frac{- 1}{3}

Divide the numbers

x = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{3}

x = 2 x = - \frac{1}{3}

x = \frac{1}{3} x = 2 x = - \frac{1}{3}

Решение

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0. \dot{3}, x_{3} = 2

Показать решение

(3x 1)(3x^2 5x 2)

Simplify the expression

Factor the expression

Find the roots