1. The problem statement, all variables and given/known data f(x) = 2x3+ax2+bx+10 When f(x)/(2x-1) the remainder is 12 When f(x)/(x+1) there is no remainder a) Find the value of a and b b) Show that f(x) = 0 has only one root 2. Relevant equations None 3. The attempt at a solution a) (2x-1)=0 x=1/2 f(1/2) = 12 = 2(1/2)3+b(1/2)2+a(1/2)+10 1/4+a/4+b/2+10=12 1+a+2b+40=48 a+2b=7 (x+1)=0 x=-1 f(-1)= 0 = 2(-1)3+a(-1)2+b(-1)+10 a-b+8=0 b=a+8 b=(7-2b)+8 b=15-2b 3b=15 b=5 a=7-2b a=7-10 a=-3 a=-3 and b=5 b) 2x3-3x2+5x+10=0 Now I need to factorise this, but I don't know how I tried using x as a common factor, but its not. 10 does not have a factor of x.