Solve x^3 -4x^2 -11x +30 - Socratic AI (ScanMath)

Question

Factor the expression

(x - 5) (x - 2) (x + 3)

Evaluate

x^{3} - 4 x^{2} - 11 x + 30

Calculate

x^{3} + x^{2} - 6 x - 5 x^{2} - 5 x + 30

Rewrite the expression

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

Factor out x from the expression

x (x^{2} + x - 6) - 5 x^{2} - 5 x + 5 \times 6

Factor out - 5 from the expression

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

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

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

Solution

More Steps

Evaluate

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

Show Solution

x_{1} = - 3, x_{2} = 2, x_{3} = 5

Evaluate

x^{3} - 4 x^{2} - 11 x + 30

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

x^{3} - 4 x^{2} - 11 x + 30 = 0

Factor the expression

(x - 5) (x - 2) (x + 3) = 0

Separate the equation into 3 possible cases

x - 5 = 0 x - 2 = 0 x + 3 = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 5 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 = 5 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 = 5 x = 2 x = - 3

Solution

x_{1} = - 3, x_{2} = 2, x_{3} = 5

Show Solution