Algebra 1

$$5t-50$$
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 $5t-50$