Question

shortcut meathods to factorise cubic polynomials​

Answer 1

Check whether your cubic contains a constant (a value).

Cubic equations take the form . However, the only essential requirement is , which means the other elements need not be present to have a cubic equation.

your equation does contain a constant (a value),

you'll need to use another solving method.If , you do not have a cubic equation.

Answer 2

Answer:

Step-by-step explanation:

Use factor theorem to find the roots of cubic equation.

possible roots are factors of constant theorem.

Once you get one root then you can use synthetic division to get the other roots.

For instance,

x³ − 6x ² + 11x − 6 = 0,

Factors of constant term are 1,2,3

for x = 1

(1)³ - 6(1)² + 11(1) - 6 = 1-6+11-6 = 12-12 = 0

So one factor is 1.

You can find other roots using factor theorem

OR

use synthetic divison

1    1     -6    11     -6

            1     -5     6

     1     -5    6       0   (1,-5,6 are co-efficient of quadratic equation)

So now we have

x³ − 6x ² + 11x − 6 = (x-1)(x²-5x+6)

(x-1)(x²-3x-2x+6)

(x-1)(x(x-3)-2(x-3))

(x-1)(x-2)(x-3)