Remainder Theorem
If polynomial p(x) of degree n>1 is divided by (x-a) where a is a constant, then the remainder is p(a)
Find minima or
... [Show More] maxima
find -b/2a and than plug back in to equation
What strategies can you use to find all the zeros of a polynomial?
synthetic division, graphing, factoring
Percent Profit Formula
Percentage Profit = ((selling price-cost price)/(cost price))*100
Polynomials
Monomial- 5x2
Binomial- 2x2+5x
Trinomial- 5x2+3x+6
The Rational Roots Test p/q
This relationship is always true: If a polynomial has rational roots, then those roots will be fractions of the form (plus-or-minus) (factor of the constant term) / (factor of the leading coefficient). However, not all fractions of this form are necessarily zeroes of the polynomial. Indeed, it may happen that none of the fractions so formed is actually a zero of the polynomial.
Find all possible rational x-intercepts of x4 + 2x3 - 7x2 - 8x + 12.
The constant term is 12, with factors of 1, 2, 3, 4, 6, and 12. The leading coefficient in this case is just 1, which makes my work a lot simpler. The Rational Roots Test says that the possible zeroes are at: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved
± 1, 2, 3, 4, 6, 12
= -12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12
Graphs of Polynomials: Predicting End Behavior of a Function
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers. So, the sign of the leading coefficient is sufficient to predict the end behavior of the function.
Graphs of Polynomials: Predicting End Behavior of a Function (2)
Polynomial End Behavior:
1. If the degree n of a polynomial is even, then the arms of the graph are either both up or both down.
2. If the degree n is odd, then one arm of the graph is up and one is down.
3. If the leading coefficient an is positive, the right arm of the graph is up.
4. If the leading coefficient an is negative, the right arm of the graph is down.
Graphs of Polynomials: Predicting End Behavior of a Function (3)
To predict the end-behavior of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative.
Graphs of Polynomials: Turning Points
Turning Points
A Turning Point is an x-value where a local maximum or local minimum happens:
How many turning points does a polynomial have?
Never more than the Degree minus 1 [Show Less]