The complete factorisation of the given polynomial equation \(3x^3-3x+5x^2-5\) can be carried out by using the arithmetic operation and after factorisation the output is \((x-1)(3x+5)(x+1)\) ,therefore, it can be say that Leo not factor the polynomial completely.
Given :
Polynomial Equation - \(3x^3-3x+5x^2-5\)
To completely factorise the given polynomial equation \(3x^3-3x+5x^2-5\) following steps can be use:
Step 1 - Rewrite the given equation.
\(=3x^3+5x^2-3x-5\)
Step 2 - Find the greatest common factor.
\(=3x^3+5x^2-3x-5\)
\(=3x^3-3x^2+8x^2-8x+5x-5\)
\(=3x^2(x-1)+8x(x-1)+5(x-1)\)
Step 3 - Take the common term out.
\(=(x-1)(3x^2+8x+5)\)
Step 4 - Now, factorise the equation \((3x^2+8x+5)\).
\(=(x-1)(3x^2+5x+3x+5)\)
\(=(x-1)(x(3x+5)+1(3x+5))\)
Step 5 - Take the common term out.
\(=(x-1)(3x+5)(x+1)\)
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
