Answer:
[tex]x^3+2x-3[/tex]
Step-by-step explanation:
the quotient of [tex](x^5 - 3x^3 - 3x^2 - 10x+15)[/tex]and a polynomial is [tex](x^2 -5)[/tex]
[tex]\frac{x^5 - 3x^3 - 3x^2 - 10x+15}{x^2-5}[/tex]
WE use long division
[tex]x^3+2x-3[/tex]
-------------------------------------------------
[tex](x^2-5)[/tex] [tex]x^5 - 0x^4-3x^3 - 3x^2 - 10x+15[/tex]
[tex]x^5 +0x^4 -5x^3[/tex]
--------------------------------------------------(subtract)
[tex]2x^3 - 3x^2-10x[/tex]
[tex]2x^3 + 0x^2 -10x[/tex]
------------------------------------------------------(subtract)
[tex]-3x^2+0x+15[/tex]
[tex]-3x^2+ 0x +15[/tex]
-----------------------------------------------------(subtract)
0
