<em>The </em><em>Remainder Theorem</em><em> states that when you divide a polynomial by a linear factor , where is a constant, the remainder is evaluated at </em>
<em>Moreover, according to the </em><em>Factor Theorem</em><em>, an extension of the Remainder Theorem, if the remainder of the function is </em><em>0</em><em> when evaluated at , then is said to be a factor of the polynomial </em>
Given the 2 theorems above, it follows that if is a factor of , then the remainder is equal to 0 when is evaluated at
We have that the total students there are 500. The 12-graders there are 200. Probability is defined as the ratio of positive outcomes of an event, over all the possible outcomes. Suppose we pick student randomly. Then, there are 200 positive outcomes (positive outcome: we pick a student in 12th grade) and there are totally 500 outcomes (we can pick 500 students in total from Riverside High School). This ratio gives: . The requested probability is 0.40