Solve 1(3x - 4)(-2x^2 - 5x^6)

Question

Simplify the expression

- 6 x^{3} - 15 x^{7} + 8 x^{2} + 20 x^{6}

Evaluate

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

Multiply the terms

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

3 x (- 2 x^{2})

Multiply the numbers

More Steps

Evaluate

3 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 3 \times 2

Multiply the numbers

- 6

- 6 x \times x^{2}

Multiply the terms

More Steps

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

Multiply the terms

More Steps

Evaluate

3 x \times 5 x^{6}

Multiply the numbers

15 x \times x^{6}

Multiply the terms

More Steps

Evaluate

x \times x^{6}

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

x^{1 + 6}

Add the numbers

x^{7}

15 x^{7}

- 6 x^{3} - 15 x^{7} - 4 (- 2 x^{2}) - (- 4 \times 5 x^{6})

Multiply the numbers

More Steps

Evaluate

- 4 (- 2)

Multiplying or dividing an even number of negative terms equals a positive

4 \times 2

Multiply the numbers

8

- 6 x^{3} - 15 x^{7} + 8 x^{2} - (- 4 \times 5 x^{6})

Multiply the numbers

- 6 x^{3} - 15 x^{7} + 8 x^{2} - (- 20 x^{6})

Solution

- 6 x^{3} - 15 x^{7} + 8 x^{2} + 20 x^{6}

Show Solution

Factor the expression

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

Evaluate

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

Multiply the terms

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

Factor the expression

More Steps

Evaluate

- 2 x^{2} - 5 x^{6}

Rewrite the expression

- x^{2} \times 2 - x^{2} \times 5 x^{4}

Factor out - x^{2} from the expression

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

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

Solution

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

Show Solution

Find the roots

x_{1} = - \frac{4 1000}{10} - \frac{4 1000}{10} i, x_{2} = \frac{4 1000}{10} + \frac{4 1000}{10} i, x_{3} = 0, x_{4} = \frac{4}{3}

Alternative Form

x_{1} \approx - 0.562341 - 0.562341 i, x_{2} \approx 0.562341 + 0.562341 i, x_{3} = 0, x_{4} = 1. \dot{3}

Evaluate

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

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

1 \times (3 x - 4) (- 2 x^{2} - 5 x^{6}) = 0

Multiply the terms

(3 x - 4) (- 2 x^{2} - 5 x^{6}) = 0

Separate the equation into 2 possible cases

3 x - 4 = 0 - 2 x^{2} - 5 x^{6} = 0

Solve the equation

More Steps

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} - 5 x^{6} = 0

Solve the equation

More Steps

Evaluate

- 2 x^{2} - 5 x^{6} = 0

Factor the expression

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

Divide both sides

x^{2} (2 + 5 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2 + 5 x^{4} = 0

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

x = 0 2 + 5 x^{4} = 0

Solve the equation

More Steps

Evaluate

2 + 5 x^{4} = 0

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

5 x^{4} = 0 - 2

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

5 x^{4} = - 2

Divide both sides

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

Divide the numbers

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

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

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

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

x = \pm 4 - \frac{2}{5}

Simplify the expression

x = \pm (\frac{4 1000}{10} + \frac{4 1000}{10} i)

Separate the equation into 2 possible cases

x = \frac{4 1000}{10} + \frac{4 1000}{10} i x = - \frac{4 1000}{10} - \frac{4 1000}{10} i

x = 0 x = \frac{4 1000}{10} + \frac{4 1000}{10} i x = - \frac{4 1000}{10} - \frac{4 1000}{10} i

x = \frac{4}{3} x = 0 x = \frac{4 1000}{10} + \frac{4 1000}{10} i x = - \frac{4 1000}{10} - \frac{4 1000}{10} i

Solution

x_{1} = - \frac{4 1000}{10} - \frac{4 1000}{10} i, x_{2} = \frac{4 1000}{10} + \frac{4 1000}{10} i, x_{3} = 0, x_{4} = \frac{4}{3}

Alternative Form

x_{1} \approx - 0.562341 - 0.562341 i, x_{2} \approx 0.562341 + 0.562341 i, x_{3} = 0, x_{4} = 1. \dot{3}

Show Solution