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

Question

Simplify the expression

4 x^{8} - 14 x^{7} + 10 x^{6}

Evaluate

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

Remove the parentheses

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

(2 x - 5) \times 2 x^{5 + 1} (x - 1)

Add the numbers

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

Multiply the first two terms

2 x^{6} (2 x - 5) (x - 1)

Multiply the terms

More Steps

Evaluate

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

2 x^{6} \times 2 x

Multiply the numbers

4 x^{6} \times x

Multiply the terms

4 x^{7}

4 x^{7} - 2 x^{6} \times 5

Multiply the numbers

4 x^{7} - 10 x^{6}

(4 x^{7} - 10 x^{6}) (x - 1)

Apply the distributive property

4 x^{7} \times x - 4 x^{7} \times 1 - 10 x^{6} \times x - (- 10 x^{6} \times 1)

Multiply the terms

More Steps

Evaluate

x^{7} \times x

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

x^{7 + 1}

Add the numbers

x^{8}

4 x^{8} - 4 x^{7} \times 1 - 10 x^{6} \times x - (- 10 x^{6} \times 1)

Any expression multiplied by 1 remains the same

4 x^{8} - 4 x^{7} - 10 x^{6} \times x - (- 10 x^{6} \times 1)

Multiply the terms

More Steps

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}

4 x^{8} - 4 x^{7} - 10 x^{7} - (- 10 x^{6} \times 1)

Any expression multiplied by 1 remains the same

4 x^{8} - 4 x^{7} - 10 x^{7} - (- 10 x^{6})

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

4 x^{8} - 4 x^{7} - 10 x^{7} + 10 x^{6}

Solution

More Steps

Evaluate

- 4 x^{7} - 10 x^{7}

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

(- 4 - 10) x^{7}

Subtract the numbers

- 14 x^{7}

4 x^{8} - 14 x^{7} + 10 x^{6}

Show Solution

Find the roots

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

Alternative Form

x_{1} = 0, x_{2} = 1, x_{3} = 2.5

Evaluate

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

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

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

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

(2 x - 5) \times 2 x^{5 + 1} (x - 1)

Add the numbers

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

Multiply the first two terms

2 x^{6} (2 x - 5) (x - 1)

2 x^{6} (2 x - 5) (x - 1) = 0

Elimination the left coefficient

x^{6} (2 x - 5) (x - 1) = 0

Separate the equation into 3 possible cases

x^{6} = 0 2 x - 5 = 0 x - 1 = 0

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

x = 0 2 x - 5 = 0 x - 1 = 0

Solve the equation

More Steps

Evaluate

2 x - 5 = 0

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

2 x = 0 + 5

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

2 x = 5

Divide both sides

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

Divide the numbers

x = \frac{5}{2}

x = 0 x = \frac{5}{2} x - 1 = 0

Solve the equation

More Steps

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}{2} x = 1

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 1, x_{3} = 2.5

Show Solution