Last updated at May 29, 2018 by Teachoo

Transcript

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)

Examples

Example 1

Example 2

Example 3 Important

Example 4

Example 5

Example 6

Example 7 Important

Example 8 Deleted for CBSE Board 2022 Exams

Example 9 Deleted for CBSE Board 2022 Exams

Example 10

Example 11

Example 12 Important

Example 13 You are here

Example 14

Example 15 Important

Example 16

Example 17

Example 18 Important

Example 19

Example 20

Example 21 Important

Example 22

Example 23 Important

Example 24 Important

Example 25 Deleted for CBSE Board 2022 Exams

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.