Given that x² -x -2 is a factor of x³ +3 x² +ax +b, calculate the values of a and b and hence find the remaining factor.

Remaining factor =

Step-by-step explanation:

Given that:

Two polynomials:

and

is a factor of .

To find:

The values of and from the cubic equation and the remaining factor.

Solution:

Let us first of all, factorize .

There are two factors of the given quadratic equation.

These two factors must also be factors of the cubic equation as well.

Putting :

Putting :

Subtracting (2) from (1):

From equation (1):

Putting the values of and in the cubic equation, we get:

Dividing the cubic equation with quadratic, we get:

constants mean the stopped points or the points on a graph that nothing is changing, hope this

step-by-step explanation: