Answer:
The quotient will be [tex](x^2+4)(x+2)[/tex]
Step-by-step explanation:
We have given the equation [tex]\frac{x^4-16}{x-2}[/tex]
We have to find the quotient
From algebraic equation we know that [tex]a^2-b^2=(a+b)(a-b)[/tex]
So [tex]\frac{x^4-16}{x-2}=\frac{(x^2)^2-4^2}{x-2}=\frac{(x^2+4)(x^2-4)}{x-2}=\frac{(x^2+4)(x+2)(x-2)}{x-2}=(x^2+4)(x+2)[/tex]
So the quotient will be [tex](x^2+4)(x+2)[/tex]
