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per3.Chapter 4 review sheet 2003

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

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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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