Question

Solve the equation x^3 + 4x^2 - 9x - 36 = 0 and show your work.

Answer 1

For the equation \(x^3 + 4x^2 - 9x - 36 = 0\), you may start by trying to find rational roots (if they exist) using factors of the constant term divided by factors of the leading coefficient. Once you find a potential root, you can apply synthetic division to check if it is a solution.

Step-by-step explanation:

hope this will help you

Answer 2

The cubic equation x^3 + 4x^2 - 9x - 36 = 0 can be solved by factoring to find a root such as x = -3, and then using the quadratic formula to find the remaining solutions from the resultant quadratic equation.

Step-by-step explanation:

To solve the cubic equation x^3 + 4x^2 - 9x - 36 = 0, we can use various methods such as factoring by grouping, synthetic division, or the rational root theorem. However, before attempting these methods, we can check if there are any obvious rational roots by using the integer root theorem which suggests trying factors of the constant term (±36).

Upon inspection, x = -3 is a root since (-3)^3 + 4(-3)^2 - 9(-3) - 36 = 0. After finding this root, we can divide the cubic polynomial by (x + 3) to get a quadratic equation, which can then be solved by factoring, completing the square, or using the quadratic formula.

After the division, we would get a quadratic equation of the form ax^2 + bx + c = 0. The solutions for this quadratic equation can then be found by applying the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a).