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Holt Algebra 1 8-3 Factoring x 2 + bx + c Warm Up 1. Which pair of factors of 8 has a sum of 9? 2. Which pair of factors of 30 has a sum of –17? Multiply. 1 and 8 r 2 – 4r – 45 –2 and –15 x 2 + 5x + 63. (x +2)(x +3) 4. (r + 5)(r – 9)

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Simplify. c.

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor quadratic trinomials of the form x 2 + bx + c. Objective

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial by guess and check. x 2 + 10x + 24

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial by guess and check. x 2 + 7x + 12

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Holt Algebra 1 8-3 Factoring x 2 + bx + c x 2 + 6x + 5 Factor each trinomial. Check your answer.

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial. Check your answer. x 2 + 6x + 9

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial. Check your answer. x 2 – 8x + 15

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial. Check your answer. x 2 – 5x + 6

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial. Check your answer. x 2 + 13x + 42

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial. Check your answer. x 2 – 13x + 40

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor x 2 + x – 20

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial. x 2 – 3x – 18

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial. Check your answer. x 2 + 2x – 15

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor each trinomial. Check your answer. x 2 – 6x + 8

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Holt Algebra 1 8-3 Factoring x 2 + bx + c X 2 – 8x – 20 Factor each trinomial. Check your answer.

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Holt Algebra 1 8-3 Factoring x 2 + bx + c A polynomial and the factored form of the polynomial are equivalent expressions. When you evaluate these two expressions for the same value of the variable, the results are the same.

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Factor y 2 + 10y + 21. Show that the original polynomial and the factored form have the same value for y = 0, 1, 2, 3, and 4.

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Holt Algebra 1 8-3 Factoring x 2 + bx + c Evaluate the original polynomial and the factored form for y = 0, 1, 2, 3, and 4. (y + 7)(y + 3) (0 + 7)(0 + 3) = 21 (1 + 7)(1 + 3) = 32 (2 + 7)(2 + 3) = 45 (3 + 7)(3 + 3) = 60 (4 + 7)(4 + 3) = 77 y 0 1 2 3 4 y 2 + 10y + 21 0 2 + 10(0) + 21 = 21 y 0 1 2 3 4 1 2 + 10(1) + 21 = 32 2 2 + 10(2) + 21 = 45 3 2 + 10(3) + 21 = 60 4 2 + 10(4) + 21 = 77 The original polynomial and the factored form have the same value for the given values of n.

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