Question

The degree of the remainder when a polynomial is divided by another polynomial is​

Answer 1

SOLUTION

TO DETERMINE

The degree of the remainder when a polynomial is divided by another polynomial

CONCEPT TO BE IMPLEMENTED

POLYNOMIAL

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

EVALUATION

For the given problem Division algorithm is applicable

Let f(x) & g(x) be two polynomials of degree n and m respectively and n ≥ m. Then there exists two uniquely determined polynomials q(x) and r(x) satisfying

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

Where the degree of q(x) is n - m and r(x) is either a zero polynomial or the degree of r(x) is less than m

So From above we can conclude that

Degree of the Remainder = 0 or less than degree of Divisor polynomial

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ 1. Real Numbers

1. using division Algorithm if 25 is

expressed as, 25 = (4xq) +r,

then the value of r is.

https://brainly.in/question/38512558

2. Use Euclid's algorithm to find the HCF of

(1) 900 and 270

(ii) 196 and 38220

Use division

https://brainly.in/question/32525059

Answer 2

Answer:

SOLUTION

TO DETERMINE

The degree of the remainder when a polynomial is divided by another polynomial

CONCEPT TO BE IMPLEMENTED

POLYNOMIAL

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

EVALUATION

For the given problem Division algorithm is applicable

Let f(x) & g(x) be two polynomials of degree n and m respectively and n ≥ m. Then there exists two uniquely determined polynomials q(x) and r(x) satisfying

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

Where the degree of q(x) is n - m and r(x) is either a zero polynomial or the degree of r(x) is less than m

So From above we can conclude that

Degree of the Remainder = 0 or less than degree of Divisor polynomial

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Real Numbers

1. using division Algorithm if 25 is

expressed as, 25 = (4xq) +r,

then the value of r is.

brainly.in/question/38512558

2. Use Euclid's algorithm to find the HCF of

(1) 900 and 270

(ii) 196 and 38220

Use division

Step-by-step explanation: