4. Factor. a) 8p2 18p 5 – – b) 24h2 20h 24 – – Solution a) 8p2 18p 5 – – Check for common factors; there are none. The product of the coefficient of and the constant term is: 8(–5) = p2 –40 Write as the sum of two terms whose coefficients have a product of –18p –40. Factors of Sum of Factors –40 1, 1 40 = –40 – –39 40 + 40 = 39 –1, –1 2, 2 20 = –20 – –18 20 + 20 = 18 –2, –2 4, 4 10 = –10 – –6 10 + 10 = 6 –4, –4 5, 5 8 = –8 – –3 8 + 8 = 3 –5, –5 The two coefficients are 2 and so write the trinomial –20, 8p2 18p 5 as 8p2 + 2p 20p 5. – – – – Remove a common factor from the 1st pair of terms, and from the 2nd pair of terms: 8p2 + 2p 20p 5 = 2p(4p + 1) 5(4p + 1) – – – Each product has a common binomial factor. 8p2 + 2p 20p 5 = (4p + 1)(2p 5) – – – So, 8p2 18p 5 = (4p + 1)(2p 5) – – – (Solution continues.)
4. Factor. a) 8p2 – 18p – 5 b) 24h2 – 20h – 24 Solution a) 8p2 – 18p – 5 Check for common factors; there are none. The product of the coefficient of p2 and the constant term is: 8(–5) = –40 Write –18p as the sum of two terms whose coefficients have a product of –40. Factors of –40 Sum of Factors 1, –40 1 – 40 = –39 –1, 40 –1 + 40 = 39 2, –20 2 – 20 = –18 –2, 20 –2 + 20 = 18 4, –10 4 – 10 = –6 –4, 10 –4 + 10 = 6 5, –8 5 – 8 = –3 –5, 8 –5 + 8 = 3 The two coefficients are 2 and –20, so write the trinomial 8p2 – 18p – 5 as 8p2 + 2p – 20p – 5. Remove a common factor from the 1st pair of terms, and from the 2nd pair of terms: 8p2 + 2p – 20p – 5 = 2p(4p + 1) – 5(4p + 1) Each product has a common binomial factor. 8p2 + 2p – 20p – 5 = (4p + 1)(2p – 5) So, 8p2 – 18p – 5 = (4p + 1)(2p – 5) (Solution continues.)
miap_ch3_notes.docx