Solve x ^ 3 + 13x ^ 2 + 32x + 20

Question

Factor the expression

(x + 1) (x + 2) (x + 10)

Evaluate

x^{3} + 13 x^{2} + 32 x + 20

Calculate

x^{3} + 12 x^{2} + 20 x + x^{2} + 12 x + 20

Rewrite the expression

x \times x^{2} + x \times 12 x + x \times 20 + x^{2} + 12 x + 20

Factor out x from the expression

x (x^{2} + 12 x + 20) + x^{2} + 12 x + 20

Factor out x^{2} + 12 x + 20 from the expression

(x + 1) (x^{2} + 12 x + 20)

Solution

More Steps

Evaluate

x^{2} + 12 x + 20

Rewrite the expression

x^{2} + (10 + 2) x + 20

Calculate

x^{2} + 10 x + 2 x + 20

Rewrite the expression

x \times x + x \times 10 + 2 x + 2 \times 10

Factor out x from the expression

x (x + 10) + 2 x + 2 \times 10

Factor out 2 from the expression

x (x + 10) + 2 (x + 10)

Factor out x + 10 from the expression

(x + 2) (x + 10)

(x + 1) (x + 2) (x + 10)

Show Solution

x_{1} = - 10, x_{2} = - 2, x_{3} = - 1

Evaluate

x^{3} + 13 x^{2} + 32 x + 20

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

x^{3} + 13 x^{2} + 32 x + 20 = 0

Factor the expression

(x + 1) (x + 2) (x + 10) = 0

Separate the equation into 3 possible cases

x + 1 = 0 x + 2 = 0 x + 10 = 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 + 10 = 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 + 10 = 0

Solve the equation

More Steps

Evaluate

x + 10 = 0

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

x = 0 - 10

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

x = - 10

x = - 1 x = - 2 x = - 10

Solution

x_{1} = - 10, x_{2} = - 2, x_{3} = - 1

Show Solution