Question

If on dividing x3 - 4x2 + 3x - 2 by a non-zero
polynomial g(x), the quotient and the remainder are
(x - 2) and -2x respectively, then g(x) is equal to
(1) x2 - 2x + 1 (2) x2 + 2x + 1
(3) x2 - 2x - 1 (4) x2 – X-1​

Answer 1

Answer:

(3) x²-2x-1

Step-by-step explanation:

p(x)= x³-4x²+3x-2

Let's take (x-2) as g(x)

So, p(2)= (2)³-4(2)²+3(2)-2= -2(2)

=> 8-16+6-2= -4

=> -4= -4

LHS=RHS

Now, checking by long division method

__________

x-2)x³-4x²+3x-2(x²-2x-1

x³-2x²

- +

----------------

-2x²+3x

-2x²+4x

+ -

----------------

-x-2

-x+2

+ -

---------

-4

--------

So, x²-2x-1 is the answer.