p(x) is a polynomial of degree …
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Dharmendra Kumar 6 years, 9 months ago
Let p(x) is a polynomial of degree 4 and g(x) is a polynomial of degree 1.
Now when p(x) is divided by g(x) the quotient is q(x) and remainder is r(x)
So by Division algorithm for polynomials we get
p(x)=q(x)×g(x)+r(x) where either r(x)=0 or degree of r(x)<degree of q(x) -----(1)
Now since p(x) is a polynomial of degree 4 and we divide it by polynomial g(x) of degree 1 ,therefore the degree of quotient q(x) must be 3.
Since r(x) cannot be 0 (given)
Therefore degree of r(x) < degree of q(x) =3 (by eq.1)
degree of r(x) < 3 so degree of r(x) is either 1 or 2.
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