CHAPTER – 2
H.C.F. AND L.C.M. OF POLYNOMIALS
GLOSSARY :
General form of a polynomial : p(x) =
an xn + an−1xn−1 + an−2xn−2 + … + a1x + a0 ,where a0 , a1, a2 ,
…
an ∈ R and an ≠ 0 , is the general form of a polynomial. In
general form of a polynomial, the exponents of the variable
may not appear systematically.
H.C.F. (Highest Common Factor) : If h(x) is a common
factor of p(x) and q(x) and every common factor of p(x) and
q(x) is a factor of h(x), then h(x) is said to be the ‘highest
common factor’ of p(x) and q(x) and is abbreviated as H.C.F. It
is denoted by h(x).
Linear polynomial : If n = 1, then the polynomial is
a1x +
a0 (where a1 ≠ 0 ). This polynomial is called ‘first degree
polynomial’ or ‘linear polynomial.’
Quadratic polynomial : If n = 2, then the polynomial is
a2x2 + a2 ≠ 0 + a1x + a0 (where a2 ≠ 0 ).This polynomial is
called ‘second degree polynomial’ or ‘linear polynomial.’
Standard form of a polynomial :
Normally, a polynomial is written in the ascending or the
descending order of exponents of the variable. The
polynomial written in either form is said to be in its ‘standard
form.’
In a polynomial, an , an−1 ,…
xn , xn−1,...x
a1 are coefficients of
respectively and
a0 is said to be the ‘constant
term.’
If a polynomial p(x) is the product of two polynomials q(x)
and r(x), then q(x) and r(x) are said to be the factors of p(x).
Zero-polynomial : 0 is called zero-polynomial. Polynomials
other than zero-polynomial are symbolically denoted by p(x),
q(x), r(x), s(x), etc.