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EXAMPLE 1 Factor when b is negative and c is positive Factor 2x2 – 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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**Factor when b is negative and c is positive**

EXAMPLE 1 Factor when b is negative and c is positive –x – 6x = –7x (x – 3)(2x – 1) 3, 1 1, 2 –3x – 2x = –5x (x – 1)(2x – 3) –1, –3 1,2 Middle term when multiplied Possible factorization Factors of 3 Factors of 2 Correct 2x2 – 7x + 3 = (x – 3)(2x – 1) ANSWER

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EXAMPLE 2 Factor when b is positive and c is negative Factor 3n2 + 14n – 5. SOLUTION Because b is positive and c is negative, the factors of c have different signs.

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**Factor when b is negative and c is positive**

EXAMPLE 2 Factor when b is negative and c is positive n – 15n = –14n (n – 5)(3n + 1) –5, 1 1, 3 –n + 15n = 14n (n + 5)(3n – 1) 5, –1 5n – 3n = 2n (n – 1)(3n + 5) –1, 5 –5n + 3n = – 2n (n + 1)(3n – 5) 1, –5 Middle term when multiplied Possible factorization Factors of –5 Factors of 3 Correct 3n2 + 14n – 5 = (n + 5)(3n – 1) ANSWER

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GUIDED PRACTICE for Examples 1 and 2 Factor the trinomial. t2 + 8t + 4 (t + 2)(3t + 2) ANSWER s2 – 9s + 5 (s – 1)(4s – 5) ANSWER h2 + 13h – 7 (h + 7)(2h – 1) ANSWER

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EXAMPLE 4 Use Descartes’ rule of signs Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for f (x) = x 6.

EXAMPLE 4 Use Descartes’ rule of signs Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for f (x) = x 6.

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