0 A Review Of Basic Algebra 1 Equations And Inequalities 2 Functions And Graphs 3 Functions 4 Polynomial And Rational Functions 5 Exponential And Logarithmic Functions 6 Linear Systems 7 Conic Sections And Quadratic Systems 8 Sequences, Series, And Probability Chapter4: Polynomial And Rational Functions
4.1 Quadratic Functions 4.2 Polynomial Functions 4.3 The Remainder And Factor Theorems; Synthetic Division 4.4 Fundamental Theorem Of Algebra And Descartes' Rule Of Signs 4.5 Zeros Of Polynomial Functions 4.6 Rational Functions 4.CR Chapter Review 4.CT Chapter Test Section4.3: The Remainder And Factor Theorems; Synthetic Division
Problem 1SC: Self Check 1 Let P(x)=2x23x+5. Find P(2) and divide P(x) by x2. What do you notice about the... Problem 2SC Problem 3SC Problem 4SC Problem 5SC Problem 6SC Problem 7SC Problem 8SC Problem 9SC Problem 1E Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E: Fill in the blanks. A shortcut method for dividing a polynomial by a binomial of the form xc is... Problem 7E Problem 8E Problem 9E: Use long division to perform each division. 2x4+x3+2x2+15x5x+2 Problem 10E Problem 11E: Find each value by substituting the given value of x into the polynomial and simplifying. Then find... Problem 12E Problem 13E: Find each value by substituting the given value of x into the polynomial and simplifying. Then find... Problem 14E: Find each value by substituting the given value of x into the polynomial and simplifying. Then find... Problem 15E: Find each value by substituting the given value of x into the polynomial and simplifying. Then find... Problem 16E: Find each value by substituting the given value of x into the polynomial and simplifying. Then find... Problem 17E: Use the Remainder Theorem to find the remainder that occurs when P(x)=3x4+5x34x22x+1 is divided by... Problem 18E Problem 19E: Use the Remainder Theorem to find the remainder that occurs when P(x)=3x4+5x34x22x+1 is divided by... Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E: Use the Remainder Theorem to find the remainder that occurs when P(x)=3x4+5x34x22x+1 is divided by... Problem 25E: Use the Factor Theorem to determine whether each statement is true. If the statement is not true, so... Problem 26E Problem 27E Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E: Use the division algorithm and synthetic division to express the polynomial function P(x)=3x32x26x4... Problem 36E Problem 37E: Use the division algorithm and synthetic division to express the polynomial function P(x)=3x32x26x4... Problem 38E Problem 39E Problem 40E Problem 41E: Use synthetic division to perform each division. x3+x2+x3x1 Problem 42E Problem 43E: Use synthetic division to perform each division. 7x33x25x+1x+1 Problem 44E Problem 45E: Use synthetic division to perform each division. 4x43x3x+5x3 Problem 46E Problem 47E Problem 48E Problem 49E: Let P(x)=5x3+2x2x+1 . Use synthetic division to find each value. P(2) Problem 50E: Let P(x)=5x3+2x2x+1 . Use synthetic division to find each value. P(2) Problem 51E: Let P(x)=5x3+2x2x+1 . Use synthetic division to find each value. P(5) Problem 52E Problem 53E Problem 54E Problem 55E: Let P(x)=2x4x2+2. Use synthetic division to find each value. P(12) Problem 56E Problem 57E: Let P(x)=2x4x2+2. Use synthetic division to find each value. P(i) Problem 58E Problem 59E: Let P(x)=x48x3+14x2+8x15. Write the terms of P(x) in descending powers of x and use synthetic... Problem 60E Problem 61E: Let P(x)=x48x3+14x2+8x15. Write the terms of P(x) in descending powers of x and use synthetic... Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E: Use the Factor Theorem and synthetic division to determine whether the given polynomial is a factor... Problem 70E Problem 71E: Use the Factor Theorem and synthetic division to determine whether the given polynomial is a factor... Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E: A partial solution set is given for each polynomial equation. Find the complete solution set.... Problem 82E Problem 83E: A partial solution set is given for each polynomial equation. Find the complete solution set.... Problem 84E Problem 85E Problem 86E Problem 87E: A partial solution set is given for each polynomial equation. Find the complete solution set.... Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E: Find a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 4,5 Problem 94E Problem 95E Problem 96E: Find a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 1,0,1 Problem 97E: Find a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 2,4,5 Problem 98E Problem 99E: Find a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 1,1,2,2 Problem 100E: Find a polynomial function P(x) with the given zeros. There is no unique answer for P(x). 0,0,0,3,3 Problem 101E Problem 102E Problem 103E Problem 104E Problem 105E Problem 106E Problem 107E Problem 108E Problem 109E Problem 110E: If 0 occurs twice as a zero of P(x)=anxn+an1xn1+...+a1x+a0, find a1. Problem 111E: If P(2)=0 and P(2)=0, explain why x24 is a factor of P(x). Problem 112E Problem 113E Problem 114E Problem 115E Problem 116E Problem 117E Problem 118E Problem 119E Problem 120E Problem 5E
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1. State the degree and the value of the leading coefficient of the polynomial function
Transcribed Image Text: 1. State the degree and the value of the leading coefficient of the polynomial function. (2 marks)
p(x)= x(x+1)* (x –1X2–x)
Degree
Leading Coefficient
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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