FACTORISING ALL TYPES Junior Cert Revision
2017 JCHL Paper 1 Question 12 (a) Factorise n 2 11n + 18. n 2 11n + 18 n 9 n 2 n 2 11n + 18 n 9 n 2 9n 2n 18 9 2 6 3 18 1 2n 9n 11n 2017 JCHL Paper 1 Question 12 (b) Factorise fully wy y 1 + w. wy y 1 + w = wy y + w 1 = y w 1 + 1 w 1 = y + 1 w 1 Factorise by Grouping
2017 JCHL Paper 1 Question 12 (d) Use factorisation to simplify 4e 2 9 2e 2 + 3e 9. Combination Factorising Factorise the top and bottom. 4e 2 9 2e 2 + 3e 9 = 2e + 3 2e 3 2e 3 e + 3 = 2e + 3 e + 3 Difference of two squares.
2016 JCHL Paper 1 Question 11 (b) Factorise each of the following expressions. (i) 25x 2 49n 2 25x 2 49n 2 = 5x + 7n 5x 7n Difference of two squares. (ii) 2x 2 9x 18 2x 2 9x 18 = 2x + 3 x 6
(b) Factorise fully ac ad bd + bc. ac ad bd + bc = ac ad + bc bd = a c d + b c d = a + b c d Factorise by Grouping
2015 JCHL Paper 1 Question 9 (a) (i) Factorise x 2 + 7x 30. x 2 + 7x 30 = x + 10 x 3
2015 JCHL Paper 1 Question 12 (a) (i) Factorise n 2 1. n 2 1 = n + 1 n 1 Difference of two squares.
2014 JCHL Paper 1 Question 4 (a) Factorise fully 9a 2 6ab + 12ac 8bc 9a 2 6ab + 12ac 8bc = 3a 3a 2b + 4c 3a 2b = 3a + 4c 3a 2b Factorise by Grouping 2014 JCHL Paper 1 Question 4 (b) Factorise 9x 2 16y 2 9x 2 16y 2 = 3x 2 4y 2 = 3x + 4y 3x 4y Difference of two squares.
2014 JCHL Paper 1 Question 4 (c) Use factors to simplify the following 2x 2 + 4x 2x 2 + x 6 Combination Factorising Factorise the top and bottom. 2x 2 + 4x 2x 2 + x 6 2x x + 2 = 2x 3 x + 2 2x = 2x 3 Common Factor
2012 JCHL Paper 1 Question 11 Factorise each of the following expressions: (i) 5x 3 10x 2 5x 3 10x 2 = 5x 2 x 2 Common Factor (ii) 4x 2 81y 2 4x 2 81y 2 = 2x + 9y 2x 9y Difference of two squares. (iii) a 2 ab + 3a 3b a 2 ab + 3a 3b = a a b + 3 a b = a + 3 a b Factorise by Grouping
FACTORISING OLD COURSE Junior Cert Revision
2013 JCHL Paper 1 Question 4 (b) (i) Factorise 8x 2 12x. 8x 2 12x = 4x 2x 3 Common Factor 2013 JCHL Paper 1 Question 4 (b) (ii) Factorise 4x 2 12x + 9. 4x 2 12x + 9 = 2x 3 2x 3 2013 JCHL Paper 1 Question 4 (b) (iii) Simplify 8x 2 12x 4x 2 12x + 9. Combination Factorising Factorise the top and bottom. 8x 2 12x 4x 2 12x + 9 = 4x 2x 3 2x 3 2x 3 = 4x 2x 3 Common Factor
2012 JCHL Paper 1 Question 3 (b) (i) Simplify 6x 2 17x + 12. 3x 4 Combination Factorising Factorise the top and bottom. 6x 2 17x + 12 3x 4 3x 4 2x 3 = 3x 4 = 2x 3 2012 JCHL Paper 1 Question 3 (b) (ii) Factorise 4c 2 3d 2cd + 6c. 4c 2 3d 2cd + 6c = 4c 2 2cd + 6c 3d = 2c 2c d + 3 2c d = 2c + 3 2c d Factorise by Grouping Rearrange 1 st.
2011 JCHL Paper 1 Question 4 (b) (i) Factorise x 2 1. x 2 1 = x + 1 x 1 Difference of two squares. 2011 JCHL Paper 1 Question 4 (b) (ii) Factorise fully ax 3 a + 3x. ax 3 a + 3x = ax a + 3x 3 = a x 1 + 3 x 1 = a + 3 x 1 Factorise by Grouping Rearrange 1 st. 2011 JCHL Paper 1 Question 4 (b) (iii) Factorise 6x 2 + x 35. = 6x 2 + x 35 = 3x 7 2x + 5
2010 JCHL Paper 1 Question 5 (b) (ii) Use factors to simplify 3x 2 19x 14 x 2. 49 Combination Factorising Factorise the top and bottom. 3x 2 19x 14 x 2 49 3x + 2 x 7 = x + 7 x 7 = 3x + 2 x + 7 Difference of two squares
2009 JCHL Paper 1 Question 6 (b)(i) Factorise 25x 2 36y 2. 25x 2 36y 2 = 5x + 6y 5x 6y Difference of two squares. 2009 JCHL Paper 1 Question 6 (b)(ii) Factorise 11x 2 + 75x 14. 11x 2 + 75x 14 = 11x 2 x + 7 2009 JCHL Paper 1 Question 6 (b)(iii) Difference of two squares. Simplify 3 4x 2 3 5x 2 3 4x 2 3 5x 2 = 3 4x + 3 5x 3 4x 3 5x = 3 4x + 3 5x 3 4x 3 + 5x = 6 9x x = 6x 9x 2
2009 JCHL Paper 1 Question 6 (b)(iii) Simplify 3 4x 2 3 5x 2 Alternate Method 3 4x 2 3 5x 2 = 3 3 4x 4x 3 4x 3 3 5x 5x 3 5x = 9 12x 12x + 16x 2 9 15x 15x + 25x 2 = 9 24x + 16x 2 9 30x + 25x 2 = 9 24x + 16x 2 9 + 30x 25x 2 = 6x 9x 2
2007 JCHL Paper 1 Question 4 (b) (i) Factorise 6c + 12bd 8d 9bc. 6c + 12bd 8d 9bc = 6c 9bc 8d + 12bd = 3c 2 3b 4d 2 3b = 3c 4d 2 3b Factorise by Grouping Rearrange 1 st. 2007 JCHL Paper 1 Question 4 (b) (ii) Reverse of Difference of two squares! Simplify 7x 2 7x + 2 5y 2 5y + 2 and fully factorise the simplified expression. 7x 2 7x + 2 5y 2 5y + 2 = 7x 2 2 2 5y 2 2 2 = 49x 2 4 25y 2 4 = 49x 2 4 25y 2 + 4 = 49x 2 25y 2 = 7x + 5y 7x 5y
2007 JCHL Paper 1 Question 4 (b) (ii) Simplify 7x 2 7x + 2 5y 2 5y + 2 and fully factorise the simplified expression. Alternate Method 7x 2 7x + 2 5y 2 5y + 2 = 7x 7x + 2 2 7x + 2 5y 5y + 2 2 5y + 2 = 49x 2 + 14x 14x 4 25y 2 + 10y 10y 4 = 49x 2 4 25y 2 4 = 49x 2 4 25y 2 + 4 = 49x 2 25y 2 = 7x + 5y 7x 5y
2006 JCHL Paper 1 Question 4 (b) (ii) Factorise 9x 2 16y 2. 9x 2 16y 2 = 3x + 4y 3x 4y Difference of two squares.
2006 JCHL Paper 1 Question 6 (b) (i) Factorise 2l kl + km 2m. 2l kl + km 2m = 2l 2m kl + km = 2 l m k l m = 2 k l m Factorise by Grouping Rearrange 1 st. 2006 JCHL Paper 1 Question 6 (b) (ii) Factorise 6x 2 19x + 10. 6x 2 19x + 10 = 3x 2 2x 5 2006 JCHL Paper 1 Question 6 (b) (iii) Factorise 17x 5x 2. 8x 2 12x = 4x 2x 3 Common Factor
2005 JCHL Paper 1 Question 3 (b) (i) Factorise 3x 2 + 8x 3. 6x 2 19x + 10 = 3x 2 2x 5 2005 JCHL Paper 1 Question 3 (b) (ii) Factorise 3p c + 3pc c 2. 3p c + 3pc c 2 = 3p + 3pc c c 2 = 3p 1 + c c 1 + c = 3p c 1 + c Factorise by Grouping Rearrange 1 st. 2005 JCHL Paper 1 Question 3 (b) (iii) Difference of two squares. Simplify 2x 1 2 x 1 2 2x 1 2 x 1 2 = 2x 1 + x 1 2x 1 x 1 = 2x 1 + x 1 2x 1 x + 1 = 3x 2 x = 3x 2 2x
2005 JCHL Paper 1 Question 3 (b) (iii) Simplify 2x 1 2 x 1 2 Alternate Method 2x 1 2 x 1 2 = 2x 2x 1 1 2x 1 x x 1 1 x 1 = 4x 2 2x 2x + 1 x 2 x x + 1 = 4x 2 4x + 1 x 2 2x + 1 = 4x 2 4x + 1 x 2 + 2x 1 = 3x 2 2x
2004 JCHL Paper 1 Question 4 (b) (i) Factorise 9x 2 64y 2. 9x 2 64y 2 = 3x + 8y 3x 8y Difference of two squares. 2004 JCHL Paper 1 Question 4 (b) (ii) Factorise 3xy 10x 10b + 3by. 3xy 10x 10b + 3by = 3xy + 3by 10x 10b = 3y x + b 10 x + b = 3y 10 x + b Factorise by Grouping Rearrange 1 st. 2004 JCHL Paper 1 Question 4 (b) (iii) Factorise 6x 2 7x 24. 6x 2 7x 24 = 3x 8 2x + 3
2003 JCHL Paper 1 Question 4 (b) (i) Factorise 4x 2 49. 4x 2 49 = 2x + 7 2x 7 Difference of two squares. 2003 JCHL Paper 1 Question 4 (b) (ii) Factorise ab cb + ac c 2. ab cb + ac c 2 = b a c + c a c = b + c a c Factorise by Grouping
2002 JCHL Paper 1 Question 3 (a) Factorise fully each of the following: (i) x 2 7x + 12 x 2 7x + 12 = x 4 x 3 (ii) 4x 2 25y 2 4x 2 25y 2 = 2x + 5y 2x 5y Difference of two squares.
2001 JCHL Paper 1 Question 3 (a) Factorise fully each of the following: (i) 20xy 4x 2 20xy 4x 2 4x 5y x Common Factor (ii) 5x 2 9x 2 5x 2 9x 2 = 5x + 1 x 2