Q. 104.1( 27 Votes )

If (y – 3) is a f

Answer :

Let f(x) = y3 – 2y2 – 9y + 18


Taking y2 common from the first two terms of f(x) and 9 from the last two terms of f(x), we get,


f(x) = y2(y – 2) –9(y – 2)


Now, taking (y – 2) common from above,


f(x) = (y2 – 9)(y – 2) -------- (A)


We know the identity as,


a2 – b2 = (a – b)(a + b)


So, using above identity on equation (A), we get,


f(x) = (y + 3)(y – 3)(y – 2)


the other two factors of y3 – 2y2 – 9y + 18 besides (y – 3) are (y + 3) and (y – 2).


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