Question

If p(x)=(x-a)q(x),then prove that degree of q(x)= degree of p(x)-1

Answer 1

hope this helps you.....

Answer 2

Concept:

Here, the concept of degree of a polynomial will be used. Comparing degree of x on both gives us the correct answer.

Given:

p(x) = (x-a) q(x)

Find:

To prove that, degree of q(x) = degree of p(x) - 1

Solution:

Here as (x-a) is multiplied by q(x), hence the degree of overall product which is equal to p(x) will be:
p(x) = q(x) + 1

∴ q(x) = p(x) - 1

Thus, the degree of q(x) = degree of p(x) - 1

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