Presentation on theme: "6.2 Polynomials and Linear Factors"— Presentation transcript:
1 6.2 Polynomials and Linear Factors At the end of this lesson, you should be able to:Factor sums and differences of cubesSolve a polynomial equation by factoringWrite a polynomial function from its zeros
2 Factoring the Sums and Differences of Cubes 13 = _23 = _33 = _43 = _53 = _63 = _73 = _83 = _93 = _103 = _1827641252163435127291000Being familiar with perfect cubes will make cubing binomials and factoring sums and differences of cubes easier.
3 Special Factoring Patterns …more know-by-♥ stuff!Special Factoring PatternsSum of Two Cubesu3 + v3 =Example:u =Difference of Two Cubesu3 - v3 =u =(u + v) (u2 - uv + v2)(u - v) (u2 + uv + v2)
4 Factor the polynomials: a. x3 - 27b. x3 - 64c. xd. xe. 4xf. 3x
6 REVIEW: Factoring By Using Combined Methods Factor the polynomial COMPLETELY:2x x2 + 12X
7 ZERO PRODUCT PROPERTY Recall: Let a and b be real numbers. If ab = 0, then a = 0 or b = 0.Alert!This property connects factoring to solving equations!
8 SOLVING POLYNOMIAL EQUATIONS BY FACTORING Solve the following equations by factoring:a. 3x4 = 48x2b. xc. 5x
9 FACTOR THEOREMYou can reverse the process and write the linear factors when you know the zeros (solutions). The relationship between the linear factors of a polynomial and the zeros of a polynomial is given by the Factor Theorem.The expression x – a is a linear factor of a polynomial if and only if the value a is a zero of the polynomial function.Write the factors of a polynomial whose zeros are 2, 2, & -3.
10 WRITING A POLYNOMIAL FUNCTION FROM ITS ZEROS Alert!A repeated zero is called a multiple zero. A multiple zero has a multiplicity equal to the number of times the zero occurs.What is the multiplicity of the polynomialfunction? Explain.
11 Final Checks for Understanding Given x3 - 4x2 = - 4x, determine the following:Factors:__________________Solutions:X-intercepts:Zeros:
12 HomeworkConnections: Zeros, Factors, and Solutions WS, plus text_______________