Question

If p(x) = 2x² +ax² + 7x -6 is divisible by 2x-1 , find a and factorise your polynomial

Answer 1

By factor theorem, If p(x)=(x-a) then p(a)=0. 2x-1=0 2x=1 X=1/2 P(1/2)=> 2(1/2)^2+a(1/2)^2+7(1/2)-6=0           => 2(1/4)+1/4a+7/2-6=0           => 1/2+1/4a+7/2-6           => 2+1+14a-24/4=0           => 14a-21/4=0           => 14a-21=0           => 14a=21           => a= 21/14                => a=3/2 Substituting the value of a in p(x). P(x)=2x^2+3/2x^2+7x-6 By remainder theorem, P(1/2)= 2(1/2)^2+3/2(1/2)^2+7(1/2)-6           =1/2+3/4+7/2-6            =2+3+14-24/4            = -5/4