2. Factorising Cubics (Example 1) Factorise x 3 + 7x 2 + 7x  15 given that (x + 3) is a factor x 3 + 7x 2 + 7x  15 = (x + 3)(x 2 + ax  5) x 3 + 7x 2 + 7x  15 = x 3 + ax 2  5x + 3x 2 + 3ax  15 Equate coefficients of x 2 7 = a + 3 a = 4 x 3 + 7x 2 + 7x  15 = (x + 3)(x 2 + 4x  5) Expand the brackets = (x + 3)(x + 5)(x  1)

3. Factorising Cubics (Example 2) Factorise 6x 3 + 7x 2  9x + 2 given that (2x  1) is a factor 6x 3 + 7x 2  9x + 2 = (2x  1)(3x 2 + ax  2) 7x 2 = 2ax 2  3x 2 Equate coefficients of x 2 7 = 2a  3 2a = 10 6x 3 + 7x 2  9x + 2 = (2x  1)(3x 2 + 5x  2) Expand the brackets for the x 2 term a = 5 =(2x  1)(3x  1)(x + 2)