Question

if y-3 is the factor y3-2y2-9y+18 then find the other two factor

Answer 1

Factor out by grouping:
y^2 (y - 2) - 9 (y - 2)
Then combine it.. making
(y^2 - 9) (y - 2)
Factoring it out again..
(y - 3) (y + 3) (y - 2)

Therefore your other factors are.. (y + 3) and (y - 2).
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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).