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# Algebra 2 Patterns in Polynomial Functions

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Expanding Polynomial Functions

Expanding Polynomial Functions

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### Transcript

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