Question

Find the value of 'a' and 'b' if (x-1) and (x+1) are the factors of p(x)=ax³-x²-bx+1.​

Answer 1

Let f(x) = ax3 + x2 − 2x + b be the given polynomial. Given (x+1) and (x-1) are factor of f (x). From factor theorem, If (x+1) and (x-1) are factors of f(x) then f(-1) = 0 and f(1) = 0 respectively.