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Objective The student will be able to:

Objective The student will be able to:. factor quadratic trinomials. Terms to remember:. Factor Trinomial Quadratic trinomial Box/Area method: (y+2)(y+4). 1) Factor. y 2 + 6y + 8. How do we decide which factors to use?. 1) Factor. y 2 + 6y + 8. (y + 2)(y + 4)

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Objective The student will be able to:

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  1. ObjectiveThe student will be able to: factor quadratic trinomials.

  2. Terms to remember: • Factor • Trinomial • Quadratic trinomial • Box/Area method: (y+2)(y+4)

  3. 1) Factor. y2 + 6y + 8 How do we decide which factors to use?

  4. 1) Factor. y2 + 6y + 8 (y + 2)(y + 4) • When the last term is positive, the factors will have the same sign as the middle term. • When the last term is negative, the factors will have different signs. • Do it! Factor: y2 - 6y + 8 • Let’s practice that next!

  5. x x x2 - 15 2) Factor. x2 - 2x - 15Change the signs of the factors! + 3 Write your solution. (x + 3)(x - 5) +3x - 5 -5x

  6. Another approach: Use a table of factors and their sums: Factor y2 + 3y – 18

  7. Another approach: Use a table of factors and their sums: Factor y2 + 3y – 18 Remember we are looking for the combination that results in a middle term of +3y. This means we need the sum of our factors to be +3.

  8. Some final advice: • Always remember to arrange your polynomial in standard form before beginning to factor. Ex. Factor 6x – 7 + x2 • Also, always check first for a possible GCF before beginning to factor. Ex: Factor 2x2y+12xy-14y

  9. Use the table of factors and their sums to match the list of trinomials to their factored form: A. y2+3y-18B. y2-3y-18C. y2-17y-18D. y2+7y -18E. y2+17y-18 F. y2-7y -18

  10. Use the table of factors and their sums to match the list of trinomials to their factored form: A. y2+3y-18B. y2-3y-18C. y2-17y-18D. y2+7y -18E. y2+17y-18 F. y2-7y -18

  11. In class practice: Factor: • a2 +12a + 27 • 14x + x2 + 45 • y4 + 5y3 - 84y2 • 2n2 - 20n + 50 • Challenge: use the results from (a) to solve a2 +12a + 27 = 0.

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