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Published byLuca Burkley Modified over 2 years ago

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EXAMPLE 1 Factor when b is negative and c is positive Factor 2x 2 – 7x + 3. SOLUTION Because b is negative and c is positive, both factors of c must be negative. Make a table to organize your work. You must consider the order of the factors of 3, because the x- terms of the possible factorizations are different.

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EXAMPLE 1 Factor when b is negative and c is positive –x – 6x = –7x(x – 3)(2x – 1) 3, 1 1, 21, 2 –3x – 2x = –5x(x – 1)(2x – 3)–1, –31,2 Middle term when multiplied Possible factorization Factors of 3 Factors of 2 Correct 2x 2 – 7x + 3 = (x – 3)(2x – 1) ANSWER

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EXAMPLE 2 Factor when b is positive and c is negative Factor 3n 2 + 14n – 5. SOLUTION Because b is positive and c is negative, the factors of c have different signs.

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EXAMPLE 2 Factor when b is negative and c is positive n – 15n = –14n(n – 5)(3n + 1)–5, 11, 3 –n + 15n = 14n(n + 5)(3n – 1)5, –11, 3 5n – 3n = 2n(n – 1)(3n + 5)–1, 51, 3 –5n + 3n = – 2n(n + 1)(3n – 5)1, –51, 3 Middle term when multiplied Possible factorization Factors of –5 Factors of 3 Correct 3n 2 + 14n – 5 = (n + 5)(3n – 1) ANSWER

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GUIDED PRACTICE for Examples 1 and 2 Factor the trinomial. 1. 3t 2 + 8t + 4(t + 2)(3t + 2) ANSWER 2. 4s 2 – 9s + 5(s – 1)(4s – 5) ANSWER 3. 2h 2 + 13h – 7 (h + 7)(2h – 1) ANSWER

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