Unit 8: Rational Functions

Key words

• Rational expressionKey word · Unit 8Rational expressionA polynomial divided by a polynomial.Exactly: A quotient $\frac{P(x)}{Q(x)}$, where $P,Q$ are polynomials and $Q(x)\ne 0$.Mix-up alert: Simplifying does not restore inputs excluded by the original denominator.See this in Key wordsClose meaning
• Excluded valueKey word · Unit 8Excluded valueAn input that the original expression does not allow.Exactly: A value outside an expression’s domain, such as a zero of an original denominator.Mix-up alert: A solution of a cleared-denominator equation can still be excluded.See this in Key wordsClose meaning
• RemainderKey word · Unit 8RemainderWhat is left after polynomial division.Exactly: In $P(x)=D(x)Q(x)+R(x)$, the remainder is zero or has smaller degree than the nonzero divisor $D$. For division by $x-c$, the remainder is $P(c)$.Mix-up alert: Use c, not -c, when dividing by x-c in synthetic division.See this in Key wordsClose meaning