[ASK] Polynomial

[Monox D. I-Fly]

The remainder of [tex]p(x)=x^3+ax^2+4bx-1[/tex] divided by [tex]x^2+1[/tex] is –5a + 4b. If the remainder of p(x) divided by x + 1 is –a – 2, the value of 8ab is ....

A. [tex]-\frac34[/tex]

B. [tex]-\frac12[/tex]

C. 0

D. 1

E. 3


Dividing p(x) by [tex]x^2+1[/tex] by [tex]x^2+1[/tex] with –5a + 4b as the remainder using long division, I got (4bx – 1) – ((a – 1)x + a – 1) = –5a + 4b, thus (4b – a + 1)x + a = –5a + 4b. Does this mean that 4b – a + 1 = 0 since the right hand doesn't have an x term? Or do I need to look for the value of x first? I'm at a loss here.