Question

y^3-2y^2-9y-18 has a factor (y-3)
then other two factors are​

Answer 1

Hi!!!

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).

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Answer 2

Answer:

(y-3)

(y+3)

(y-2)

are factors of y³-2y²-9y-18