Question

On a test, leo is asked to completely factor the polynomial 3x3 – 3x 5x2 – 5. he uses double grouping to get (x2 – 1)(3x 5). has he factored the polynomial completely? explain.

Answer 1

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).

Answer 2

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.