Answer:
The factors of the polynomial are (x+1), (2x-3) and (x -1)
Explanation:
Here, we want to know the linear factors of the function.
What we simply want to calculate are those factors when multiplied with each other gives the polynomial in question.
We start by looking at the polynomial itself, we discover that the polynomial in question is a polynomial of degree three. What this means is that the polynomial will have three roots.
In this kind of question, we make use of testing.
Testing in the sense that since we know that the factor of a polynomial if substituted in that polynomial will give no remainder( 0)
So let’s say we start with one of the options (x-1)
We set this to 0
x -1 = 0
This implies that x = 1
So make a substitution of x= 1 in the polynomial
We will get;
2(1)^3 - 3(1)^2 -2(1) + 3 = 2-3-2+3 = 0
This means that (x-1) is actually a factor
The next thing to do is to use the polynomial long division; That will be;
(2x^3 − 3x^2 − 2x + 3)/ (x-1)
This gives ;
2x^2 -x -3
We can now proceed to factorize the quadratic equation;
That will be;
2x^2 + 2x -3x -3
= 2x(x + 1) -3( x + 1)
So the factors are;
(2x-3)(x+ 1)
These are the two other factors aside (x-1)