Question

if (y-3) is a factor of ycube-2y-9y+18 then find the other two factors

Answer 1

Divide y cube - 2y-9y+18 by y-3

Answer 2

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,

a^2 – b^2 = (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).