Polynomial question (1 Viewer)

jxballistic · Sep 8, 2012

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

Timothy6340 · Sep 8, 2012

is the answer 3 ?/

jxballistic · Sep 8, 2012

Timothy6340 said:
is the answer 3 ?/

its 1/2

asianese · Sep 8, 2012

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 $\\ 3(-\frac{1}{2})-1=a\\ \therefore a=-\frac{5}{2}$

shongaponga · Sep 9, 2012

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

Polynomial question (1 Viewer)

jxballistic

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Timothy6340

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asianese

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