Solve (3x-4)(2x 1)(x^2)(x 1)

Question

Simplify the expression

6 x^{5} - 8 x^{4}

Evaluate

(3 x - 4) (2 x \times 1) x^{2} (x \times 1)

Remove the parentheses

(3 x - 4) \times 2 x \times 1 \times x^{2} \times x \times 1

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

(3 x - 4) \times 2 x^{1 + 2 + 1}

Add the numbers

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

Multiply the terms

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

Apply the distributive property

2 x^{4} \times 3 x - 2 x^{4} \times 4

Multiply the terms

More Steps

Evaluate

2 x^{4} \times 3 x

Multiply the numbers

6 x^{4} \times x

Multiply the terms

More Steps

Evaluate

x^{4} \times x

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

x^{4 + 1}

Add the numbers

x^{5}

6 x^{5}

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

Solution

6 x^{5} - 8 x^{4}

Show Solution

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

Alternative Form

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

Evaluate

(3 x - 4) (2 x \times 1) (x^{2}) (x \times 1)

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

(3 x - 4) (2 x \times 1) (x^{2}) (x \times 1) = 0

Multiply the terms

(3 x - 4) \times 2 x (x^{2}) (x \times 1) = 0

Calculate

(3 x - 4) \times 2 x \times x^{2} (x \times 1) = 0

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

(3 x - 4) \times 2 x^{1 + 2 + 1}

Add the numbers

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

Multiply the terms

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

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

x = 0 3 x - 4 = 0

Solve the equation

More Steps

Evaluate

3 x - 4 = 0

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

3 x = 0 + 4

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

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

x = 0 x = \frac{4}{3}

Solution

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

Alternative Form

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

Show Solution