Rational Functions of Expressions are ratios (or quotients) of polynomials. They are processed exactly like fractions. Polynomials in standard form are sums of powers of the variable. Numbers in decimal representation are sums of powers of $10$. Polynomials are processed much like numbers, except that you cannot trade some powers of $x$ for a higher power of $x$. Thus the manipulation of polynomials is in some ways actually easier than the corresponding manipulation of decimal numbers! An example for this fact is provided by long division.
Use long division with remainder to complete the blanks below. Remember that some of the coefficients may be negative.
$2x^3 +2x^2+5x-5 = (x^2-x+2) \times ($ $x +$ $) +$ $x$ $+$ .