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

Question

Simplify the expression

3 x^{3} - 15 x^{2} - 2 x^{6} + 10 x^{5}

Evaluate

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

Apply the distributive property

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

Multiply the terms

More Steps

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}

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

Multiply the numbers

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

Multiply the terms

More Steps

Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

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

Multiply the numbers

3 x^{3} - 15 x^{2} - 2 x^{6} - (- 10 x^{5})

Solution

3 x^{3} - 15 x^{2} - 2 x^{6} + 10 x^{5}

Show Solution

Factor the expression

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

Evaluate

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

Solution

More Steps

Evaluate

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

Rewrite the expression

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

Factor out x^{2} from the expression

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

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

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 12}{2}, x_{3} = 5

Alternative Form

x_{1} = 0, x_{2} \approx 1.144714, x_{3} = 5

Evaluate

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

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

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

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

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

3 - 2 x^{3} = 0

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

- 2 x^{3} = 0 - 3

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

- 2 x^{3} = - 3

Change the signs on both sides of the equation

2 x^{3} = 3

Divide both sides

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

Divide the numbers

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

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

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

Calculate

x = 3 \frac{3}{2}

Simplify the root

x = \frac{3 12}{2}

x = 0 x = \frac{3 12}{2}

x = 0 x = \frac{3 12}{2} x - 5 = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 0 x = \frac{3 12}{2} x = 5

Solution

x_{1} = 0, x_{2} = \frac{3 12}{2}, x_{3} = 5

Alternative Form

x_{1} = 0, x_{2} \approx 1.144714, x_{3} = 5

Show Solution