Question

When a polynomial 3xcube + 2xsquare + ax + b is divided by (x + 2) leaves remainder 4 and (x-3) leave remainder -1.Find a & b

Answer 1

Answer:

a=-24 and b= -28

Step-by-step explanation:

Concept used:

Remainder theorem:

The remainer when P(x) is divided by (x-a) is P(a)

Let $P(x)=3x^3+2x^2+ax+b$

The remainder when P(x) is divided by (x+2) is 4

That is P(-2)=4

$3(-2)^3+2(-2)^2+a(-2)+b=4\\\\-24+8-2a+b=4\\\\-2a+b=20..............(1)$

The remainder when P(x) is divided by (x-3) is -1

That is P(3)=-1

$3(3)^3+2(3)^2+a(3)+b=-1\\\\81+18+3a+b=-1\\\\3a+b=-100..............(2)$

-2a+b=20..............(1)

3a+b=-100..............(2)

(1)-(2)

-5a=120

a=-24

put a=-24 in (1) we get

-2(-24)+b=20

48+b=20

b=-28