Answer:
Leo does not factored the polynomial completely.
3x^3-3x+5x^2-5=(x+1)(x-1)(3x+5)
Step-by-step explanation:
Given: On a test, Leo is asked to completely factor the polynomial
3x^3-3x+5x^2-5.
also, he uses double grouping to get (x^2- 1)(3x+5)
We have to explain whether he factored the polynomial completely or not.
Consider the given polynomial 3x^3-3x+5x^2-5.
after double grouping he get (x^2- 1)(3x+5)
Also, we can simplify further ,
Using algebraic identity a^2-b^2=(a+b)(a-b)
We get,
(x^2- 1)=(x+1)(x-1)
We get, (x^2- 1)(3x+5)=(x+1)(x-1)(3x+5)
Thus, 3x^3-3x+5x^2-5=(x+1)(x-1)(3x+5)
Thus, He does not factored the polynomial completely.
