Polynomial help please! (1 Viewer)

[aoniumz]

When a polynomial is divided by (2x+1)(x-3), the remainder is 3x-1. What is the remainder when the polynomial is divided by 2x+1

 

[Carrotsticks]

Hint: Since we are dividing by a quadratic, the remainder will be in the form ax+b, where a and b can be any real numbers.

 

[aoniumz]

P(x) = (2x+1)(x-3) Q(x) + 3x-1

P(x)= (2x+1) Q(x) + ax+b

idk what I am doing

 

[MrBeefJerky]

Correct me if I'm wrong, but don't u just sub P(-1/2) into P(x)=(2x+1)(x-3)Q(x)+3x-1

 

[bonnychoho]

-2.5

 

[Carrotsticks]

Oh sorry, I mis-read your question. It's a lot simpler than I had originally thought. I processed it as one of those typical 'When P(x) is divided by (2x-1) the remainder is 3, when P(x) is divided by (x+1) the remainder is -1, what is the remainder when P(x) is divided by (2x-1)(x+1) etc', where the usual step would be to let the remainder by ax+b.

P(-1/2) = 0 + 3(-1/2)-1 since P(x) = (2x+1)(x-3) Q(x) + 3x-1.

 

[aoniumz]

Well, answer at the back of my book says 1/2 lol
and yes the question I posted is the right question..

 

[braintic]

Well, answer at the back of my book says 1/2 lol
and yes the question I posted is the right question..

It would be 1/2 if the remainder given was -3x-1 .....

 

[aoniumz]

Guess it was just a typo