Please suggest me a easy shortcut method to factorise cubic equations .
Sure! One popular shortcut method to factorize cubic equations is by using the Rational Root Theorem and synthetic division. Here's a step-by-step guide:
Step 1: Write the cubic equation in the form: ax^3 + bx^2 + cx + d = 0.
Step 2: Use the Rational Root Theorem to determine possible rational roots. The possible rational roots can be found by taking the factors of the constant term (d) divided by the factors of the leading coefficient (a).
Step 3: Use synthetic division to test the possible rational roots. Start by testing the first possible rational root and divide the cubic equation by (x - r), where r is the possible root. Perform synthetic division and check if the remainder is zero.
Step 4: If the synthetic division yields a remainder of zero, the tested rational root is a factor of the cubic equation. The resulting quotient will be a quadratic equation.
Step 5: Factorize the resulting quotient from Step 4 using common methods like factoring, completing the square, or using the quadratic formula.
Step 6: The factored quadratic equation will give you the remaining factors of the cubic equation.
Step 7: Repeat Steps 3 to 6 if necessary to find all the factors of the cubic equation.
Using this shortcut method, you can factorize cubic equations more efficiently and quickly by identifying possible rational roots and applying synthetic division.