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

Question

Simplify the expression

3 x^{3} - 15 x^{5} - 2 x^{2} + 10 x^{4}

Evaluate

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

Apply the distributive property

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

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}

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

Multiply the terms

More Steps

Evaluate

3 x \times 5 x^{4}

Multiply the numbers

15 x \times x^{4}

Multiply the terms

More Steps

Evaluate

x \times x^{4}

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

x^{1 + 4}

Add the numbers

x^{5}

15 x^{5}

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

Multiply the numbers

3 x^{3} - 15 x^{5} - 2 x^{2} - (- 10 x^{4})

Solution

3 x^{3} - 15 x^{5} - 2 x^{2} + 10 x^{4}

Show Solution

Factor the expression

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

Evaluate

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

Factor the expression

More Steps

Evaluate

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

Rewrite the expression

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

Factor out x^{2} from the expression

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

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

Solution

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

Show Solution

Find the roots

x_{1} = - \frac{5}{5}, x_{2} = 0, x_{3} = \frac{5}{5}, x_{4} = \frac{2}{3}

Alternative Form

x_{1} \approx - 0.447214, x_{2} = 0, x_{3} \approx 0.447214, x_{4} = 0. \dot{6}

Evaluate

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

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

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

3 x - 2 = 0

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

3 x = 0 + 2

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

3 x = 2

Divide both sides

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

Divide the numbers

x = \frac{2}{3}

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

Solve the equation

More Steps

Evaluate

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

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

1 - 5 x^{2} = 0

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

- 5 x^{2} = 0 - 1

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

- 5 x^{2} = - 1

Change the signs on both sides of the equation

5 x^{2} = 1

Divide both sides

\frac{5 x ^{2}}{5} = \frac{1}{5}

Divide the numbers

x^{2} = \frac{1}{5}

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

x = \pm \frac{1}{5}

Simplify the expression

x = \pm \frac{5}{5}

Separate the equation into 2 possible cases

x = \frac{5}{5} x = - \frac{5}{5}

x = 0 x = \frac{5}{5} x = - \frac{5}{5}

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

Solution

x_{1} = - \frac{5}{5}, x_{2} = 0, x_{3} = \frac{5}{5}, x_{4} = \frac{2}{3}

Alternative Form

x_{1} \approx - 0.447214, x_{2} = 0, x_{3} \approx 0.447214, x_{4} = 0. \dot{6}

Show Solution