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Example 13 - Factorise 6x2 + 17x + 5 by splitting the - Examples

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Example 13 (Splitting the middle term) Factorise 6x2 + 17x + 5 by splitting the middle term, and by using the Factor Theorem. 6x2 + 17x + 5 We factorize using the splitting the middle term method = 6x2 + 2x + 15x + 5 = 2x(3x + 1) + 5(3x + 1) = (3x + 1) (2x + 5) Example 13 (Factor Theorem) Factorise 6x2 + 17x + 5 by splitting the middle term, and by using the Factor Theorem. Step 1: We check if x2 is multiplied by 1. 6x2 + 17x + 5 = 6 ("x2 + " 17/6 " x + " 5/6) = 6 p(x) Step 2: We factorize p(x) Let "x2 + " 17/6 " x + " 5/6 = (x – a) (x – b) So, ab = Constant term = 5/6 We find factors of 5/6 5/6 = 5/6 × 1 5/6 = 5/3 × 1/2 5/6 = 5/2 × 1/3 So, factors of 5/6 are 1, 5/3 , 5/2, 1/3 , 1/2 We take value of x as 1, 5/3 , 5/2, 1/3 , 1/2 –1, (−5)/3 , (−5)/2, (−1)/3 , (−1)/2 and check value of p(x) i.e. "x2 + " 17/6 " x + " 5/6 Hence, a = (−5)/2 , b = (−1)/3 Now, "x2 + " 17/6 " x + " 5/6 = (x – a) (x – b) = ("x – " ((−5)/2))("x – " ((−1)/3)) = ("x + " 5/2) ("x + " 1/3) So, 6x2 + 17x + 5 = 6 ("x2 + " 17/6 " x + " 5/6) = 6 ("x + " 5/2) ("x + " 1/3) = 6 ((2𝑥 + 5)/2) ((3𝑥 + 1)/3) = (2𝑥 + 5) (3𝑥 + 1)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.