Question

solution of question no. 3 of exercise 2.3 of book ncert of class 9

Answer 1

given that 2xsquare-3x+5 is divided by 2x-3
therefore x=2/3

=f (x)=2xsquare-3x+5
=f (2/3)=2 (3/2)square-3 (3/2)+5
=3/2-9/2+5
=-6/2+5
=-6+10/2
=2.
let see 2 divided it or not.

=2 (2)square-3 (2)+5
=6-6+5
=5.
no 2 does not divides it.

Answer 2

☛ Factor Theorem ;

If p ( x ) is a polynomial of degree ≥ one and a is any real number , then

( i ) ( x - a ) is a factor of p ( x ) , if p ( a ) = 0.

( ii ) p ( a ) = 0, if ( x - a ) is a factor of p (x).


☛ Remainder Theorem ;

Division and Algorithm for polynomials : If p(x) and g(x) are two polynomials with g(x) ≠ 0, then we can find q ( x ) and r (x) and such that

p ( x ) = g ( x ) * q ( x ) + r ( x ), where
r (x) = 0 (or) deg r(x) < deg g(x)

Dividend = Divisor × quotient + remainder