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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 degrees of p(x) and g(x)

Solution:

Given, a polynomial p(x) is divided by a polynomial g(x).

The remainder r(x) is zero.

We have to find the relation between the degrees of p(x) and g(x).

The division algorithm states that given any polynomial p(x) and any non-zero

polynomial g(x), there are polynomials q(x) and r(x) such that

p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

p(x) = g(x) q(x) + (0)

Degree of p(x) = degree of g(x) (or)

Degree of p(x) > degree of g(x)

Therefore, the relation is that the degree of p(x) is greater than the degree of g(x).

✦ Try This: If on division of a polynomial t(x) by a polynomial s(x), the remainder is zero, what is the relation between the degrees of r(x) and s(x)

Given, a polynomial t(x) is divided by a polynomial s(x).

The remainder r(x) is zero.

We have to find the relation between the degrees of r(x) and s(x).

The division algorithm states that given any polynomial p(x) and any non-zero

polynomial g(x), there are polynomials q(x) and r(x) such that

p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

t(x) = s(x) q(x) + (0)

Degree of t(x) = degree of s(x) (or)

Degree of t(x) > degree of s(x)

Therefore, the relation is that the degree of t(x) is greater than the degree of s(x)

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.2 Problem 1 (iv)

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 degrees of p(x) and g(x)

Summary:

If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, the relation between the degrees of p(x) and g(x) is that the degree of p(x) is greater than the degree of g(x)

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