Example 1. Without actual division prove that
x⁴+2x³-2x²+2x-3 is divisible by x²+2x-3
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Firstly factorise....(x^2+2x-3)
x^2+3x-x-3
x(x+3) -1(x+3)
(x+3) (x-1)
now,
the value of p(x)= x+3=0
=x=-3 and
p(x)=x-1=0=x=1
put the value of x in the polynomial p(x) one by one
x^2+3x-x-3
x(x+3) -1(x+3)
(x+3) (x-1)
now,
the value of p(x)= x+3=0
=x=-3 and
p(x)=x-1=0=x=1
put the value of x in the polynomial p(x) one by one
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