Solve (3x-4)(2x^2-3x^5)

Question

Simplify the expression

6 x^{3} - 9 x^{6} - 8 x^{2} + 12 x^{5}

Evaluate

(3 x - 4) (2 x^{2} - 3 x^{5})

Apply the distributive property

3 x \times 2 x^{2} - 3 x \times 3 x^{5} - 4 \times 2 x^{2} - (- 4 \times 3 x^{5})

Multiply the terms

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Evaluate

3 x \times 2 x^{2}

Multiply the numbers

6 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}

6 x^{3}

6 x^{3} - 3 x \times 3 x^{5} - 4 \times 2 x^{2} - (- 4 \times 3 x^{5})

Multiply the terms

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Evaluate

3 x \times 3 x^{5}

Multiply the numbers

9 x \times x^{5}

Multiply the terms

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Evaluate

x \times x^{5}

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

x^{1 + 5}

Add the numbers

x^{6}

9 x^{6}

6 x^{3} - 9 x^{6} - 4 \times 2 x^{2} - (- 4 \times 3 x^{5})

Multiply the numbers

6 x^{3} - 9 x^{6} - 8 x^{2} - (- 4 \times 3 x^{5})

Multiply the numbers

6 x^{3} - 9 x^{6} - 8 x^{2} - (- 12 x^{5})

Solution

6 x^{3} - 9 x^{6} - 8 x^{2} + 12 x^{5}

Show Solution

Factor the expression

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

Evaluate

(3 x - 4) (2 x^{2} - 3 x^{5})

Factor the expression

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Evaluate

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

Rewrite the expression

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

Factor out x^{2} from the expression

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

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

Solution

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

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Find the roots

x_{1} = 0, x_{2} = \frac{3 18}{3}, x_{3} = \frac{4}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.87358, x_{3} = 1. \dot{3}

Evaluate

(3 x - 4) (2 x^{2} - 3 x^{5})

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

(3 x - 4) (2 x^{2} - 3 x^{5}) = 0

Separate the equation into 2 possible cases

3 x - 4 = 0 2 x^{2} - 3 x^{5} = 0

Solve the equation

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Evaluate

3 x - 4 = 0

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

3 x = 0 + 4

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

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

x = \frac{4}{3} 2 x^{2} - 3 x^{5} = 0

Solve the equation

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Evaluate

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

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

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Evaluate

2 - 3 x^{3} = 0

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

- 3 x^{3} = 0 - 2

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

- 3 x^{3} = - 2

Change the signs on both sides of the equation

3 x^{3} = 2

Divide both sides

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

Divide the numbers

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

Take the 3 -th root on both sides of the equation

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

Calculate

x = 3 \frac{2}{3}

Simplify the root

x = \frac{3 18}{3}

x = 0 x = \frac{3 18}{3}

x = \frac{4}{3} x = 0 x = \frac{3 18}{3}

Solution

x_{1} = 0, x_{2} = \frac{3 18}{3}, x_{3} = \frac{4}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.87358, x_{3} = 1. \dot{3}

Show Solution