Question

what must be added to p(x)=4x 4 +2x 3 -2x 2 +x-1 so that the resulting polynomial is divisible by g(x)=x 2 +2x-3

Answer 1

Hi,

p( x )= 4x⁴+ 2x³- 2x²+x -1

g(x )= x²+2x-3

x²+2x-3)4x⁴+2x³-2x²+x-1(4x²-6x+22

4x⁴+8x³-12x²
______________________
-6x³+10x²+x

-6x³-12x²+18x
___________________

22x²-17x-1

____________________
-61x+65

The remainder = -61x +65

Now we have to add 61x -65 to p(x)

So that the resulting polynomial is

divisible by g( x )

I hope this helps you.

:)

Answer 2

Given ,

P(x) = 4X4 + 2X3 - 2x2 + x + 1

G(x) = x2 + 2x - 3

Now , P(x) ÷ G(x)

So , by dividing p(x) by g(x)

, we get

Remainder = -61 + 65

Now we have to add 61x - 65 to p(x) .

So, that the resulting polynomial is divisible by G(x).

THANKS FOR ASKING THIS QUESTION.

I HOPE THIS HELPS YOU.

IF THIS HELPS YOU THEN GIVE ME 5 5 STARS.

BYE SEE U SOON.