Common Core Algebra I Exponential Function Assessment

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹).

Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (𝘹² + 𝘺²)² = (𝘹² – 𝘺²)² + (2𝘹𝘺)² can be used to generate Pythagorean triples.

Rewrite simple rational expressions in different forms; write 𝘢(𝘹)/𝘣(𝘹) in the form 𝘲(𝘹) + 𝘳(𝘹)/𝘣(𝘹), where 𝘢(𝘹), 𝘣(𝘹), 𝘲(𝘹), and 𝘳(𝘹) are polynomials with the degree of 𝘳(𝘹) less than the degree of 𝘣(𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system.