1. ## Polynomial question

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

does anyone know how to solve this?
I tried p(-1/2) = 0 + 3*(-1/2) -1 = -5/2 but that's not the right answer

3. ## Re: Polynomial question

Originally Posted by Timothy6340
its 1/2

4. ## Re: Polynomial question

Are you sure?

$P(x)&=(x-3)(2x+1)Q(x)+3x-1 by the division transformation \\ &=(2x+1)S(x) +a for some polynomials S(x) and Q(x), and a constant a.\\ \therefore (x-3)(2x+1)Q(x)+3x-1=(2x+1)S(x)+a\\ Setting x =-\frac{1}{2} yields \\ 3(-\frac{1}{2})-1=a\\ \therefore a=-\frac{5}{2}$

5. ## Re: Polynomial question

I also get the remainder as -5/2. Could just be a mistake in the answers

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