About this worksheet: This worksheet is meant to allow the teacher to grade for correct answers quickly and accurately without grading every single problem by hand. You should tell the students that the dots will not form a picture like they are used to. The students do need to use a straightedge when connecting the dots.
Perform arithmetic operations on polynomials.
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.
Understand the relationship between zeros and factors of 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).
Rewrite rational expressions.
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.