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Pre-Calculas
| Term | Definition |
|---|---|
| Remainder Theorem | If f(X) is divided by (x-c), then the remainder is f(c) |
| Factor Theorem | given a polynomial function, f(x), x-c is a factor of f(x) if and only if f(c) =0 |
| fundamental Theorem of algebraic | a polynomial of degree n has n complex roots (real and nonreal bots) some of these may be repeated roots |
| Linear factorization Theorem | if f(x) is a polynomial function of degree n>0, then f(x) has precisely n linear factors + f(x)=a(x-z)(x-z2) (x-zn) where a is the leading coefficient of f(x) and z, z2, are the complex zeros of f(x). the zi are not distinct nth |
| complex conjugate | the complex conjugate of a and bi, where a and b are real numbers, is a-bi |
| Conjugate pairs | the numbers a+bi and a-bi, where a and b are real numbers, are referred to a conjugate pair. |
| Rational zeros Theorem | If p(x) =anx^n +an-1 a1,a0 are real numbers and n is a positive integer; then all rational zeros of p(x) is of the form p/q where p is a factor of an and q is a factor of a0 |
| P | a factor of the leading coefficient of a polynomial |
| q | a factor of the constant term of polynomial |
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