No, Leo's answer is not a product of prime polynomials because x2 – 1 can be factored. This is a difference of squares. He should continue factoring to get
(x – 1)(x + 1)(3x + 5).
The complete factorisation of the given polynomial equation [tex]3x^3-3x+5x^2-5[/tex] can be carried out by using the arithmetic operation and after factorisation the output is [tex](x-1)(3x+5)(x+1)[/tex] ,therefore, it can be say that Leo not factor the polynomial completely.
Given :
Polynomial Equation - [tex]3x^3-3x+5x^2-5[/tex]
To completely factorise the given polynomial equation [tex]3x^3-3x+5x^2-5[/tex] following steps can be use:
Step 1 - Rewrite the given equation.
[tex]=3x^3+5x^2-3x-5[/tex]
Step 2 - Find the greatest common factor.
[tex]=3x^3+5x^2-3x-5[/tex]
[tex]=3x^3-3x^2+8x^2-8x+5x-5[/tex]
[tex]=3x^2(x-1)+8x(x-1)+5(x-1)[/tex]
Step 3 - Take the common term out.
[tex]=(x-1)(3x^2+8x+5)[/tex]
Step 4 - Now, factorise the equation [tex](3x^2+8x+5)[/tex].
[tex]=(x-1)(3x^2+5x+3x+5)[/tex]
[tex]=(x-1)(x(3x+5)+1(3x+5))[/tex]
Step 5 - Take the common term out.
[tex]=(x-1)(3x+5)(x+1)[/tex]
From the above steps it can be concluded that Leo does not factor the polynomial completely.
For more information, refer the link given below:
https://brainly.com/question/20293447
