Solve (2x-1)(x-4)(x-2)

Question

Simplify the expression

2 x^{3} - 13 x^{2} + 22 x - 8

Evaluate

(2 x - 1) (x - 4) (x - 2)

Multiply the terms

More Steps

Evaluate

(2 x - 1) (x - 4)

Apply the distributive property

2 x \times x - 2 x \times 4 - x - (- 4)

Multiply the terms

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

Multiply the numbers

2 x^{2} - 8 x - x - (- 4)

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

2 x^{2} - 8 x - x + 4

Subtract the terms

More Steps

Evaluate

- 8 x - x

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

(- 8 - 1) x

Subtract the numbers

- 9 x

2 x^{2} - 9 x + 4

(2 x^{2} - 9 x + 4) (x - 2)

Apply the distributive property

2 x^{2} \times x - 2 x^{2} \times 2 - 9 x \times x - (- 9 x \times 2) + 4 x - 4 \times 2

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}

2 x^{3} - 2 x^{2} \times 2 - 9 x \times x - (- 9 x \times 2) + 4 x - 4 \times 2

Multiply the numbers

2 x^{3} - 4 x^{2} - 9 x \times x - (- 9 x \times 2) + 4 x - 4 \times 2

Multiply the terms

2 x^{3} - 4 x^{2} - 9 x^{2} - (- 9 x \times 2) + 4 x - 4 \times 2

Multiply the numbers

2 x^{3} - 4 x^{2} - 9 x^{2} - (- 18 x) + 4 x - 4 \times 2

Multiply the numbers

2 x^{3} - 4 x^{2} - 9 x^{2} - (- 18 x) + 4 x - 8

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

2 x^{3} - 4 x^{2} - 9 x^{2} + 18 x + 4 x - 8

Subtract the terms

More Steps

Evaluate

- 4 x^{2} - 9 x^{2}

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

(- 4 - 9) x^{2}

Subtract the numbers

- 13 x^{2}

2 x^{3} - 13 x^{2} + 18 x + 4 x - 8

Solution

More Steps

Evaluate

18 x + 4 x

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

(18 + 4) x

Add the numbers

22 x

2 x^{3} - 13 x^{2} + 22 x - 8

Show Solution

Find the roots

x_{1} = \frac{1}{2}, x_{2} = 2, x_{3} = 4

Alternative Form

x_{1} = 0.5, x_{2} = 2, x_{3} = 4

Evaluate

(2 x - 1) (x - 4) (x - 2)

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

(2 x - 1) (x - 4) (x - 2) = 0

Separate the equation into 3 possible cases

2 x - 1 = 0 x - 4 = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

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

Divide the numbers

x = \frac{1}{2}

x = \frac{1}{2} x - 4 = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = \frac{1}{2} x = 4 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = \frac{1}{2} x = 4 x = 2

Solution

x_{1} = \frac{1}{2}, x_{2} = 2, x_{3} = 4

Alternative Form

x_{1} = 0.5, x_{2} = 2, x_{3} = 4

Show Solution