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Question
If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?
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Solution
We know that,
p(x) = g(x) × q(x) + r(x)
According to the question,
q(x) = 0
When q(x) = 0, then r(x) is also = 0
So, now when we divide p(x) by g(x),
Then p(x) should be equal to zero
Hence, the relation between the degrees of p(x) and g(x) is the degree p(x) < degree g(x).
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