Polynomials

Question 1

Division of Polynomials by degree:

Answer 1

What it is called (degree):
Constant Polynomial (degree 0)
Linear Polynomial (degree 1)
Quadratic Polynomial(degree 2)
Cubic Polynomial ( degree 3)
Biquadratic Polynomial (degree
5)

Question 2

Methods for finding HCF of Polynomials:

Answer 2

Step 1: Express each polynomial
as a product of powers
of irreducible factors
which also requires the
numerical factors
to be expressed as the
product of the powers of primes.
Step 2: If there is no common
factor then HCF is 1 and
if there are common
irreducible factors, we
find the least
exponent of these
irreducible factors in the
factorized form of the
given polynomials.
Step 3: Raise the common
irreducible factors to the
smallest or the least
exponents found in step
2 and take their
product to get the HCF.

Question 3

Methods for finding LCM of Polynomials:

Answer 3

Step 1: First express each
polynomial as a product
of powers of irreducible
factors.
Step 2: Consider all the
irreducible factors (only
once) occurring in the
given polynomials. For
each of these factors,
consider the greatest
exponent in the
factorized form of the
given polynomials.
Step 3: Now raise each
irreducible factor to the
greatest exponent and
multiply them to get the
LCM.

Question 4

HCF vs LCM of Polynomials :

Answer 4

HCF x LCM = Product of Polynomials

Answer 5

Rational Number with Polynomials :