text: 1) Plug -1 in for x and simplify.  f(-1) is the remainder.  \nf(-1) = a(-1)^3 + (a+b)(-1)^2 + (a+2b)(-1) + 1\nf(-1) = -a + a + b - a - 2b + 1\nf(-1) = -a - b + 1\nIf it is exactly divisible then the remainder must be 0.\n-a - b + 1 = 0 or b = 1-a\n\n2) i)Show that P(1) and P(-1) equal 0.\nii) Use long division to obtain\n(b+4)x + (a+6)\nb+4 = 2, so b = -2\na+6 = 3, so a = -3\niii) P(x) is divisible by x^2-1 so the remainder is 0.\n3(0) + 4(2x+3) = 8x + 12\nCheck my work.