Question

find the value of p if( x-p) is a factor of x^5-p^2x^3+2x+p+3 hence, factorise x^2+4px+3

Answer 1

Answer:

Given (x-p) is the factor of x^5-p²x³+2x+p+3 => p^5 -p²(p)³+2(p)+p+3=0 => p^5 -p^5+2p +p+3=0 => 3p +3=0 =>3p= -3 => p= -1 We know x-p=0 x=p => x= -1 Substitute this in the given second eq x²+4px+3 (-1)²+4p(-1) +3=0 1-4p +3=0 -4p +4=0 -4p=-4 p=1