Chapter 2 · Question 6

State the division algorithm for polynomials and explain the meaning of quotient and remainder.

Answer

Direct Answer

If

p(x)

and

g(x)

are polynomials with

g(x)\ne0

, then

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

, where

q(x)

is the quotient and either

r(x)=0

or degree of

r(x)

is less than degree of

g(x)

.

Simple Explanation

It is like long division: dividend equals divisor times quotient plus remainder.

Exam-Ready Structure

For polynomials

p(x)

and

g(x)

,

g(x)\ne0

, there exist polynomials

q(x)

and

r(x)

such that

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

, where

r(x)=0

or

\deg r(x)<\deg g(x)

. Here

p(x)

is the dividend,

g(x)

is the divisor,

q(x)

is the quotient, and

r(x)

is the remainder.

Key Points

If $p(x)$ and $g(x)$ are polynomials with $g(x)\ne0$ , then $p(x)=g(x)q(x)+r(x)$ , where $q(x)$ is the quotient and either $r(x)=0$ or degree of $r(x)$ is less than degree of $g(x)$ .

State the division algorithm for polynomials and explain the meaning of quotient and remainder.

Answer

Direct Answer

Simple Explanation

Exam-Ready Structure

Key Points

Related Questions

Define the degree of a polynomial. Distinguish between linear, quadratic, and cubic polynomials.

What is a zero of a polynomial? Find the zero of $p(x)=2x-6$ .

State the division algorithm for polynomials and explain the meaning of quotient and remainder.

Answer

Direct Answer

Simple Explanation

Exam-Ready Structure

Key Points

Related Questions

Define the degree of a polynomial. Distinguish between linear, quadratic, and cubic polynomials.

What is a zero of a polynomial? Find the zero of p(x)=2x−6p(x)=2x-6p(x)=2x−6.

What is a zero of a polynomial? Find the zero of $p(x)=2x-6$ .