If $(2x^2-7x+9)/f(x) = (2x-3)$ with a remainder of 3, what is $f(x)$ ?

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Answer 1 · 2015-11-01T09:15:49

$f(x) = x - 2$

When D is divided by d, quotient is q and remainder is r.

$D = dq + r \Rightarrow d = \frac{D - r}{q}$

$D = 2x^2 - 7x + 9$

$q = 2x - 3$

$r = 3$

$\Rightarrow f = d = \frac{2x^2-7x + 9 - 3}{2x - 3} = x -2$

If (2x^2-7x+9)/f(x) = (2x-3)(2x^2-7x+9)/f(x) = (2x-3) with a remainder of 3, what is f(x)f(x)?