Answer
$$5t-50$$
Work Step by Step
In order to divide a polynomial by a binomial, there must be a term for every power between the highest and lowest powers. To do this, add a placeholder of $0t$.
$$(5t^2+0t-500)\div(t+10)$$
In order to match the first term of the dividend, $5t^2$, multiply the divisor by $5t$. The $5t$ will go on top of your division sign.
$$(5t)(t+10)=5t^2+50t$$
Subtract this from the first two terms of the dividend
$$(5t^2+0t-500)-(5t^2+50t)=-50t$$
Bring down the next term of the dividend.
$$-50t-500$$
Multiply the divisor by $-50$ to match this. The $-50$ will follow the $5t$ on top of your division sign.
$$(-50)(t+10)=-50t-500$$
Subtract this from the dividend. Since this results in zero, you have no remainder and a final answer of $5t-50$
