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# Algebra 2 Patterns in Polynomial Functions

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Expanding Polynomial Functions

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### Algebra 2 Patterns in Polynomial Functions

1. 1. Warm up <ul><li>Simplify </li></ul>
2. 2. Relationships between the roots and coeffients of polynomials
3. 3. Group 1 <ul><li>Expand the polynomial functions: </li></ul><ul><ul><li>P 4 = (x – a)(x – b)(x – c)(x – d) </li></ul></ul><ul><ul><li>Write down all of the terms with x 3 only </li></ul></ul><ul><ul><li>Examine the terms with x 3 and determine the pattern by using the roots to find the coefficient of the x 3 term </li></ul></ul><ul><ul><li>Then write down all of the constant terms and determine how to determine the constant term in general. </li></ul></ul>
4. 4. Group 2 <ul><li>Expand the polynomial functions: </li></ul><ul><ul><li>P 4 = (x – a)(x – b)(x – c)(x – d) </li></ul></ul><ul><ul><li>Write down all of the terms with x 2 only </li></ul></ul><ul><ul><li>Examine the terms with x 2 and determine the pattern by using the roots to find the coefficient of the x 2 term </li></ul></ul>
5. 5. Group 3 <ul><li>Expand the polynomial functions: </li></ul><ul><ul><li>P 4 = (x – a)(x – b)(x – c)(x – d) </li></ul></ul><ul><ul><li>Write down all of the terms with x only </li></ul></ul><ul><ul><li>Examine the terms with x and determine the pattern by using the roots to find the coefficient of the x term </li></ul></ul>
6. 6. Group 4 <ul><li>Expand the polynomial functions: </li></ul><ul><ul><li>P 5 = (x – a)(x – b)(x – c)(x – d)(x – e) </li></ul></ul><ul><ul><li>Write down all of the terms with x 3 only </li></ul></ul><ul><ul><li>Examine the terms with x 3 and determine the pattern by using the roots to find the coefficient of the x 3 term </li></ul></ul>
7. 7. Group 5 <ul><li>Expand the polynomial functions: </li></ul><ul><ul><li>P 5 = (x – a)(x – b)(x – c)(x – d)(x – e) </li></ul></ul><ul><ul><li>Write down all of the terms with x 2 only </li></ul></ul><ul><ul><li>Examine the terms with x 2 and determine the pattern by using the roots to find the coefficient of the x 2 term </li></ul></ul>
8. 8. Group 6 <ul><li>Expand the polynomial functions: </li></ul><ul><ul><li>P 5 = (x – a)(x – b)(x – c)(x – d)(x – e) </li></ul></ul><ul><ul><li>Write down all of the terms with x 4 only </li></ul></ul><ul><ul><li>Examine the terms with x and determine the pattern by using the roots to find the coefficient of the x term </li></ul></ul>
9. 9. On you board <ul><li>Write your polynomial function in factored form </li></ul><ul><li>Write your assigned terms </li></ul><ul><li>Illustrate or describe how to use the roots to determine the coefficient of your variable. </li></ul>