1. Give an example of a single polynomial with degree 3, whose value is 4 when the variable is equal to 1.

2. Give an example of a single polynomial with degree 3, whose value is 29 when the variable is equal to 2.

3. Find a polynomial with degree 3 whose values are 4 and 29 when the variable is equal to 1 and 2, respectively. How many polynomials that satisfy these constraints are there? Note that in this part, you need to come up with a single polynomial that satisfies these two constraints simultaneously.

4. State the identities of the difference of two squares and the square of a binomial. Why do you think they are important? give at least one example from each identity.