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What will the quotient and remainder be on division of ax² + bx + c by px³ + qx² + rx + s, p≠0

Solution:

Given, ax² + bx + c is divided by px³ + qx² + rx + s, p≠0

We have to find the quotient and remainder.

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).

Here, p(x) = ax² + bx + c

g(x) = px³ + qx² + rx + s

Degree of p(x) = 2

Degree of g(x) = 3

Since, the degree of g(x) is greater than the degree of p(x) (3 > 2)

The quotient on dividing p(x) by q(x) will be zero

The remainder will be the dividend itself.

Therefore, the quotient will be zero and the remainder will be ax² + bx + c.

✦ Try This: What will the quotient and remainder be on division of rx² + sx + u by

ax³ + bx² + cx + d, a≠0

Given, rx² + ax + u is divided by ax³ + bx² + cx + d, a≠0

We have to find the quotient and remainder

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).

Here, p(x) = rx² + sx + u

g(x) = ax³ + bx² + cx + d

Degree of p(x) = 2

Degree of g(x) = 3

Since, the degree of g(x) is greater than the degree of p(x) (3 > 2)

The quotient on dividing p(x) by q(x) will be zero

The remainder will be the dividend itself.

Therefore, the quotient will be zero and the remainder will be rx² + sx + u

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

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

Summary:

The quotient and remainder on division of ax² + bx + c by px³ + qx² + rx + s, p≠0 be zero and ax² + bx + c respectively.

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