Q. 1 D3.6( 15 Votes )
If on division of a non - zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degree of p (x) and g (x)?
g(x) is the factor of p(x) and degree of p(x) degree of g(x)
Here r(x) = 0
By division algorithm,
p(x) = g(x)q(x) + r(x)
p(x) = g(x) q(x)
∴ deg(p(x)) = deg(g(x))×deg(q(x))
⇒ deg(p(x))≥ deg(g(x))
Hence g(x) is the factor of p(x) and clearly degree of p(x) degree of g(x)
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