Question

quadratic polynomial divided by (x-1),(x+2) gives the remainder 6,30 respectively and it is divisible by (x-3) then find polynomial.​

Answer 1

Step-by-step explanation:

Thne polynomial is quadratic, means it has 2 factors.

Question says (x-1) and (x+2) are exactly divisible, means they are it's factors.

That's it!

The polynomial is,

(x - 1)(x + 2) = {x}^{2} +2x - x - 2 \\ = {x}^{2} + x - 2

Note: I don't why the question says about (x+3) and reminder 4. May to confuse. But if you divide the above answer with (x+3), you will get a reminder = 4

Hope this helps

Answer 2

since polynomial is exactly divisible by (X - 3)

according to question

(x - 1 + 6)(x +2 +30)

= (x+5)(x+32)

= x^2 + 37x + 160

so the polynomial is

x^2 +32x +160