Solve x^3+6x^2+11x+6

Question

Factor the expression

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

Evaluate

x^{3} + 6 x^{2} + 11 x + 6

Calculate

x^{3} + 5 x^{2} + 6 x + x^{2} + 5 x + 6

Rewrite the expression

x \times x^{2} + x \times 5 x + x \times 6 + x^{2} + 5 x + 6

Factor out x from the expression

x (x^{2} + 5 x + 6) + x^{2} + 5 x + 6

Factor out x^{2} + 5 x + 6 from the expression

(x + 1) (x^{2} + 5 x + 6)

Solution

More Steps

Evaluate

x^{2} + 5 x + 6

Rewrite the expression

x^{2} + (3 + 2) x + 6

Calculate

x^{2} + 3 x + 2 x + 6

Rewrite the expression

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

Factor out x from the expression

x (x + 3) + 2 x + 2 \times 3

Factor out 2 from the expression

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

Factor out x + 3 from the expression

(x + 2) (x + 3)

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

Show Solution

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

Evaluate

x^{3} + 6 x^{2} + 11 x + 6

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

x^{3} + 6 x^{2} + 11 x + 6 = 0

Factor the expression

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

Separate the equation into 3 possible cases

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

Solution

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

Show Solution