#### Question

Find the number that must be subtracted from the polynomial 3y^{3} + y^{2} – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.

#### Solution

Let the number to be subtracted from the given polynomial be k

let` f(y)=3y^3+y^2-22y+15-k `

it is given that f(y) is divisible by` (y+3) `

Remainder=`f(-3) =0 `

`3(-3)^3+(-3)^2-22(-3) +15-k=0 `

`-81+9+66+15-k=0 `

`9-k=0`

`k=9 `

Is there an error in this question or solution?

Solution Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3. Concept: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.