Solve 4x^(3)-2x^(2)-24x-18

Question

Factor the expression

2 (x - 3) (x + 1) (2 x + 3)

Evaluate

4 x^{3} - 2 x^{2} - 24 x - 18

Rewrite the expression

2 \times 2 x^{3} - 2 x^{2} - 2 \times 12 x - 2 \times 9

Factor out 2 from the expression

2 (2 x^{3} - x^{2} - 12 x - 9)

Factor the expression

More Steps

Evaluate

2 x^{3} - x^{2} - 12 x - 9

Calculate

2 x^{3} + 5 x^{2} + 3 x - 6 x^{2} - 15 x - 9

Rewrite the expression

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

Factor out x from the expression

x (2 x^{2} + 5 x + 3) - 3 \times 2 x^{2} - 3 \times 5 x - 3 \times 3

Factor out - 3 from the expression

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

Factor out 2 x^{2} + 5 x + 3 from the expression

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

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

Solution

More Steps

Evaluate

2 x^{2} + 5 x + 3

Rewrite the expression

2 x^{2} + (3 + 2) x + 3

Calculate

2 x^{2} + 3 x + 2 x + 3

Rewrite the expression

x \times 2 x + x \times 3 + 2 x + 3

Factor out x from the expression

x (2 x + 3) + 2 x + 3

Factor out 2 x + 3 from the expression

(x + 1) (2 x + 3)

2 (x - 3) (x + 1) (2 x + 3)

Show Solution

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

Alternative Form

x_{1} = - 1.5, x_{2} = - 1, x_{3} = 3

Evaluate

4 x^{3} - 2 x^{2} - 24 x - 18

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

4 x^{3} - 2 x^{2} - 24 x - 18 = 0

Factor the expression

2 (x - 3) (x + 1) (2 x + 3) = 0

Divide both sides

(x - 3) (x + 1) (2 x + 3) = 0

Separate the equation into 3 possible cases

x - 3 = 0 x + 1 = 0 2 x + 3 = 0

Solve the equation

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 x + 1 = 0 2 x + 3 = 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 = 3 x = - 1 2 x + 3 = 0

Solve the equation

More Steps

Evaluate

2 x + 3 = 0

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

2 x = 0 - 3

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

2 x = - 3

Divide both sides

\frac{2 x}{2} = \frac{- 3}{2}

Divide the numbers

x = \frac{- 3}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{3}{2}

x = 3 x = - 1 x = - \frac{3}{2}

Solution

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

Alternative Form

x_{1} = - 1.5, x_{2} = - 1, x_{3} = 3

Show Solution