pre calc 2.5--2.7 terms Flashcards
Fundamental theorem of algebra
If f(X) is a polynomial of degree “n” where n>0, then f has at least one zero in the complex number system
PRODUCT OF LINEAR FACTORS
Separating the equation into factors
Rational zero test
P/Q
*where P is the constant and Q is the leading coefficient
Descartes’s Rule of Signs
Positive: number of positive real zeros of F is equal to or less than the number of variations in the signs
Negative: number of negative real zeros of F is equal to or less than the number of variations in the signs
“Irreducible over the reals”
When reduced, whether it’s imaginary or real
When you have a positive number and get all positive numbers, you have an
UPPER bound (so don’t test any numbers higher than that)
When you have a negative number and get all negative numbers, you have a
LOWER bound (so don’t test any numbers lower than that)
Conjugate pairs
Positives pair with negatives
Example: (A+Bi) (A-Bi)
Rational function
A quotient of polynomial functions; can be written in the form
f(X) = N(X) / D(X)
where N(X) and D(X) are polynomials and D(X) is not zero
Vertical asymptote
Whatever makes the denominator equal zero
If the numerator degree is less than the denominator degree, what is the horizontal asymptote?
The X axis
If the numerator degree is equal to the denominator degree, what is the horizontal asymptote?
The ratio of the leading coefficients
If the numerator degree is greater than the denominator degree by ONE, what is the horizontal asymptote?
The quotient; you have to divide the equation
(slant)
If the numerator degree is greater than the denominator degree by TWO, what is the horizontal asymptote?
Quotient is a parabolic asymptote
Indeterminant form
0/0
