per3.Chapter 4 review sheet 2003

per3.Chapter 4 review sheet 2003 - Look at the sign of the...

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Chapter 4 – Polynomial Equations and Inequalities 4.1- Solving Polynomial Equations To solve a polynomial equation there are several strategies, you can use the factor theorem factor by grouping solve graphically using TOV, transformations or a graphing calculator Ex: Factor by grouping: Graphically: f(x)= x 3 + x 2 - 4x - 4 = x 2 (x+1) -4 (x+1) = (x 2 -4) (x+1) = (x + 2)(x-2)(x+1) 4.2 – Solving Linear Inequalities Inequality notation includes: <, >, When solving, use opposite/inverse operations When multiplying or dividing by a negative number you have to inverse the inequality sign: o Example:     -2x-1>-1 -2x >-1+1 -2x >0 -2x < 0 -2 -2 x< 0 When there is a double inequality you must inverse the operations and apply to each part 4.3 – Solving Polynomial Inequalities To solve a polynomial inequality algebraically: Determine the roots of the polynomial equation. Do this by: 1. Moving all the terms to one side of the inequality 2. Factoring the polynomial to determine the zeros of the polynomial equation
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Unformatted text preview: Look at the sign of the polynomial in each of the intervals created at these roots The solution is determined by the interval(s) that satisfy the inequality given in the question Using a number line, graph, or a factor table to determine the intervals on which the polynomial is positive or negative. o Example: Say you have (x + 3) (x - 3) (x + 2) > 0, the factor table will look like: Intervals (-, -3) (-3, -2) (-2, 3) (3, ) Test Value-4-2.5 1 4 (x + 3) + + + (x 3) + + (x + 2) + Sign of f(x) + + x (-3, -2) U (3, ) 4.4 Rates of Change in Polynomial Functions The average rate of change of a polynomial function y = f(x) on the interval from x1 x x2 is: AROC=f(x2)-f(x1) x2-x1 This allows you to find the slope of the secant The instantaneous rate of change of a polynomial y=f(x) at x=a can be found with the IROC or difference quotient formula IROC= f(a+h) f(a) h This allows you to find the slope of the tangent...
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This note was uploaded on 01/14/2012 for the course MAT 107 taught by Professor Sda during the Spring '11 term at Beacon FL.

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per3.Chapter 4 review sheet 2003 - Look at the sign of the...

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