Question

please ANSWER THIS ASAP

Answer 1

Answer:

Let P(X) = $3x^{3} -8x^{2} +3x+2$

Let G(X) = (X²-3X+2) = (X²-2X-X+2)

=> X(X-2) -1(X-2)

=> (X-2) (X-1).

Now, P(X) will be exactly divisible by G(X) if it is exactly divisible by (X-2) as well as (X-1).

Putting X = 2 in P(X).

P(X) =$3x^{3} -8x^{2} +3x+2$

P(2) = ( 3 × 23 - 8 × 22 + 3 × 2 +  2)

=> (24-32+6+2) = (24-24) = 0

And,

P(1) = (3 × 13 -8 × 12 + 3 × 1 +2)

=> (3-8+3+2) = (5-5) = 0

Therefore,

P(X) is exactly divisible by (X-2) and (X-1)

So , P(X) is exactly divisible by (X²-3X+2)

Hence,

P(X) is exactly divisible by (X²-3X+2)