Solve x^3-13x-12 - ScanMath

Question

Factor the expression

(x - 4) (x + 1) (x + 3)

Evaluate

x^{3} - 13 x - 12

Calculate

x^{3} + 4 x^{2} + 3 x - 4 x^{2} - 16 x - 12

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 4 from the expression

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

Factor out x^{2} + 4 x + 3 from the expression

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

Solution

More Steps

Evaluate

x^{2} + 4 x + 3

Rewrite the expression

x^{2} + (3 + 1) x + 3

Calculate

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

Rewrite the expression

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

Factor out x from the expression

x (x + 3) + x + 3

Factor out x + 3 from the expression

(x + 1) (x + 3)

(x - 4) (x + 1) (x + 3)

Show Solution

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

Evaluate

x^{3} - 13 x - 12

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

x^{3} - 13 x - 12 = 0

Factor the expression

(x - 4) (x + 1) (x + 3) = 0

Separate the equation into 3 possible cases

x - 4 = 0 x + 1 = 0 x + 3 = 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 = 4 x + 1 = 0 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 = 4 x = - 1 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 = 4 x = - 1 x = - 3

Solution

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

Show Solution