Sec3 A Maths

kkhing SG

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 SG

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

kkhing SG

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 SG

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 SG

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.