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Factoring Trinomials x 2 + bx + c CORD Math Mrs. Spitz Fall 2006

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Objectives Students will learn how to factor trinomials with the following pattern: x 2 + bx + c

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Assignment Worksheets as provided

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What does a factored trinomial look like? (x )(x ) Look at the trinomial. Are the signs positive, negative or both positive and negative. For example: x 2 + 12x + 27 ++ What are the factors of 27 that add to give you 12? 1 +27 = 28 3 +9 = 12 39 Both signs are positive meaning you are looking for factors of 27 that add to give you 12—the number in the middle. With no coefficient (the number in front of the variable x 2 (the letter), it’s pretty easy to figure out.

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Factor x 2 +14x + 45 14 45 What are the factors of 45 that add to give you 14? 1 +45 = 46 3 +15 = 18 5 +9 = 14 5 9 + Format of factored trinomial is: (x + 5)(x + 9)

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Trinomials—Let’s try this out! Tri meaning three referring to the number of terms Examples:

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What does a factored trinomial look like? (x )(x ) Look at the trinomial. Are the signs positive, negative or both positive and negative. For example: x 2 + 22x + 21 ++ What are the factors of 21 that add to give you 22? 1 +21 = 22 3 +7 = 10 1 21 Both signs are positive meaning you are looking for factors of 21 that add to give you 22—the number in the middle. With no coefficient (the number in front of the variable x 2 (the letter), it’s pretty easy to figure out.

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Factor t 2 – 2t – 63 -2 -63 What are the factors of 63 that subtract to give you -2? 1 - 63 = -62 3 – 21 = -18 7 - 9 = -2 7 9 - Format of factored trinomial is: (t + 7)(t - 9) With two negatives, you are looking for a positive and a negative number to multiply to give you a negative 63.

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Factor m 2 – 9m + 20 -9 20 What are the factors of 20 that add to give you 20? -1 – 20 = -21 -2 – 10 = -12 -4 – 5 = -9 -4 5 - Format of factored trinomial is: (m - 4)(m - 5) With a negative in front and a positive in back, you are looking for two negative factors that add to give you negative 9 and multiply to give a positive 20.

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Factor r 2 + 4r - 21 (r )(r ) Look at the trinomial. The first is positive, the second negative meaning you are looking for factors of 21 that subtract to give you a positive 4. +- What are the factors of 21 that subtract to give you 4? 21 - 1 = 20 7 – 3 = 4 7 3 Format of factored trinomial is: (r + 7)(r - 3)

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