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Pre calculus
UE2
| Term | Definition |
|---|---|
| Rational Zeros Theorem | If p(x)= anx^n + an-1x^n-1...is a polynomial, where an, an-1....are real numbers n= positive all rational zeroes p(x) |
| Remainder theorem | f(x) is divided by (x-c) then is f(c) |
| factor theorem | given poly function f(x), (x-c) is factor of f(x) if only f(c) = 0 |
| Fundamental theorem of algebra | poly of degree n has n complex roots (real and non-real roots) *may be repeated* |
| Linear Factorization Theorem | f(x) is poly. function degree n>0 then f(x) precisely n linear functions and f(x) and Z1, Z2...Zn are complex zeroes of f(x) Zi are not necessary distinct numbers, maybe repeated |
| Complex Conjugate | of a number a+bi, where a fb are real numbers is a-bi |
| Conjugate pairs | number a+bi and a-bi, where a fb are real numbers are referred to as a conjugate pair |
| Polynomial Inequality | where both sides of inequality are poly. expression |
| Solution Set | set all real numbers of x, inequality is true |
| Sign Set | chat created along number line, zeroes are marked, includes x test point each interval between zeroes, as well as sign of f(x) for each interval |
| Interval notation | set notation describe union of intervals, open parenthesis and signify x include endpoint of interval and closed parentheisis signify endpoint of interval |
| Rational Inequality | an inequality in which one or both sides is a raational expression |
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