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**1. Homework Statement**

Let f, g be nonzero polynomials with deg (f) [tex]\geq[/tex] deg (g). Show that there

is a unique monomial bx[tex]^{k}[/tex] where deg(f(x) - bx[tex]^{k}[/tex]g(x)) < deg (f).

**2. Homework Equations**

see above

**3. The Attempt at a Solution**

I define polynomials f and g, with deg(f) = n and deg (g) = m and n[tex]\geq[/tex]m

and let the monomial be h(x) so h(x)g(x) = l(x) and using the theorem deg(h(x)g(x)) = deg(h(x)+g(x)) and therefore deg l(x) = k + m. so overall i have to find deg(f(x)-l(x)) but this is equal to f(x) not less than f(x), how do I show its less than f(x).