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

Question

Simplify the expression

6 x^{7} - 16 x^{6} + 10 x^{5}

Evaluate

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

Multiply the terms

More Steps

Evaluate

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

Apply the distributive property

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

Multiply the terms

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Evaluate

2 x^{5} \times 3 x

Multiply the numbers

6 x^{5} \times x

Multiply the terms

6 x^{6}

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

Multiply the numbers

6 x^{6} - 10 x^{5}

(6 x^{6} - 10 x^{5}) (x - 1)

Apply the distributive property

6 x^{6} \times x - 6 x^{6} \times 1 - 10 x^{5} \times x - (- 10 x^{5} \times 1)

Multiply the terms

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Evaluate

x^{6} \times x

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

x^{6 + 1}

Add the numbers

x^{7}

6 x^{7} - 6 x^{6} \times 1 - 10 x^{5} \times x - (- 10 x^{5} \times 1)

Any expression multiplied by 1 remains the same

6 x^{7} - 6 x^{6} - 10 x^{5} \times x - (- 10 x^{5} \times 1)

Multiply the terms

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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}

6 x^{7} - 6 x^{6} - 10 x^{6} - (- 10 x^{5} \times 1)

Any expression multiplied by 1 remains the same

6 x^{7} - 6 x^{6} - 10 x^{6} - (- 10 x^{5})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

6 x^{7} - 6 x^{6} - 10 x^{6} + 10 x^{5}

Solution

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Evaluate

- 6 x^{6} - 10 x^{6}

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

(- 6 - 10) x^{6}

Subtract the numbers

- 16 x^{6}

6 x^{7} - 16 x^{6} + 10 x^{5}

Show Solution

Find the roots

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

Alternative Form

x_{1} = 0, x_{2} = 1, x_{3} = 1. \dot{6}

Evaluate

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

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

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

Multiply the terms

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

Elimination the left coefficient

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

Separate the equation into 3 possible cases

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

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

x = 0 3 x - 5 = 0 x - 1 = 0

Solve the equation

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Evaluate

3 x - 5 = 0

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

3 x = 0 + 5

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

3 x = 5

Divide both sides

\frac{3 x}{3} = \frac{5}{3}

Divide the numbers

x = \frac{5}{3}

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

Solve the equation

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Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 0 x = \frac{5}{3} x = 1

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 1, x_{3} = 1. \dot{6}

Show Solution