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

Question

Simplify the expression

4 x^{4} - 3 x^{3} - 8 x + 6

Evaluate

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x^{3} \times 4 x

Use the commutative property to reorder the terms

4 x^{3} \times x

Multiply the terms

More Steps

Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

4 x^{4}

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

Use the commutative property to reorder the terms

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

Multiply the numbers

4 x^{4} - 3 x^{3} - 8 x - (- 2 \times 3)

Multiply the numbers

4 x^{4} - 3 x^{3} - 8 x - (- 6)

Solution

4 x^{4} - 3 x^{3} - 8 x + 6

Show Solution

x_{1} = \frac{3}{4}, x_{2} = 32

Alternative Form

x_{1} = 0.75, x_{2} \approx 1.259921

Evaluate

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

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

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

x^{3} - 2 = 0

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

x^{3} = 0 + 2

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

x^{3} = 2

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

3 x^{3} = 32

Calculate

x = 32

x = 32 4 x - 3 = 0

Solve the equation

More Steps

Evaluate

4 x - 3 = 0

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

4 x = 0 + 3

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

4 x = 3

Divide both sides

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

Divide the numbers

x = \frac{3}{4}

x = 32 x = \frac{3}{4}

Solution

x_{1} = \frac{3}{4}, x_{2} = 32

Alternative Form

x_{1} = 0.75, x_{2} \approx 1.259921

Show Solution