Sec3 A Maths

• kkhing

  17 Jul 12, 17:23

  Hi,

  Can someone help me with this question? Thanks.

  Q1. Show that x-2y is a factor of x^3+2x^2 y-5xy^2-6y^3 and find the other two factors.

• FireIce

  17 Jul 12, 17:32

  chg all the x to 2y. the result = 0 show's tt x-2y is a factor
• kkhing

  17 Jul 12, 17:42

  I already done the first part, but what about the 2nd parts - the other 2 factors? i got no clue at all? Please help.

• Jx7909

  17 Jul 12, 18:11

  x^3 + 2x^2y - 5xy^2 - 6y^3 = (x - 2y) (x^2 + axy + 3y^2)

   

  Comparing coeffs of y^2,

  -5x = 3x - 2ax

  8x = 2ax

  a = 4

  x^2 + 4xy + 3y^2 = (x + 3y) (x + y)

  Two factors: x + 3y, x + y

  Hope that helps.

• SBS n SMRT

  23 Jul 12, 00:11

  actually all the above not show method, but "verify", use factor Thm to be safe, f(2y) = 0. Fireice one can but needs the rigour of factor thm to be safe.