Intermediate Algebra Practice Set #1

Here are some interesting Intermediate Algebra problems:

These problems are suggested for students completing Algebra II or for those starting Precalculus. However, there may be some Algebra whizzes out there too, so give these problems a try! 🙂

To check your answers, comment below at the bottom of the page. I will respond if it is correct or not.

1. If and , what is the value of ?
2. If a polynomial has roots 1, 3, 5, and 7, then what is the sum of the coefficients of this polynomial?
3. What’s the probability if  and are the numbers rolled by the two fair six-sided dice such that ?
4. Evaluate .
5. Factor completely over the integers.

Challenge Problem:

Six positive integers are written on the faces of a cube. Each vertex is labeled with the product of the three numbers on the faces adjacent to the vertex. If the sum of the numbers on the vertices is equal to 1001, then what is the sum of the numbers written on the faces?