The quotient of (x^5-3x^3-3x^2-10x+15) and a polynomial is (x^2-5). What is the polynomial

The operation this problem requires is multiplication. In this case, you need to multiply the quotient by the huge polynomial given.

The problem will be: (x^2-5) (x^5-3x^3-3x^2-10x+15)

When it comes to this, you have to distribute. First you need to distribute the x^2 to the big polynomial, then distribute the - 5 to the big polynomial. After that you have to combine the two big polynomials into one by combining the like terms.

Therefore, the new polynomial should be the following:

x^7-3x^5-3x^4-10x^3 + 15x^2-5x^5+15x^3+15x^2+50x-75

x^7-8x^5-3x^4+5x^3+30x^2+50x-75

That would be the final answer.