[emerald000]

Originally Posted by SKG_Scintill

You know what, why make another thread about a single question.
This is completely unrelated to the OP, but it's just another math question.

I have no idea how to do this, and sadly, neither does my teacher
I don't know all the technical math in english, so bear with me...

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Define at the given polynomial f(x) and the given number "a" a polynomial g(x) and a number "b" in such a way that f(x) = (x - a)g(x) + b

f(x) = 2x^2 + 3, a = 1
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This is how far I get:
2x^2 + 3 = (x - 1)g(x) + b

...After that I just get entangled in the quadratic formula.

2x^2 + 3 = (x - 1)g(x) + b
2x^2 + 3 - b = (x - 1)g(x)

Since 2x^2 + 3 - b is a second degree polynomial and (x - 1) is a first degree polynomial, g(x) will be a first degree polynomial in the form of cx + d.

(cx + d)(x - 1) = 2x^2 + 3 - b
cx^2 - cx + dx - d = 2x^2 + 3 - b

So c = 2. That leaves:

2x^2 - 2x + dx - d = 2x^2 + 3 - b
(d - 2)x - d = 3 - b

So d = 2. That leaves:

(2 - 2)x - 2 = 3 - b
-2 = 3 - b
b = 5

So g(x) = 2x + 2 and b = 5.