Question

If both x + 1 and x − 1 are factors of ax³ + x² − 2x + b, find the values of a and b.

Answer 1

Let be the given polynomial.

By factor theorem, if and both are factors of the polynomial f (x). if f(−1) and f(1) both are equal to zero.

Therefore,

And

Adding (i) and (ii), we get

And putting this value in equation (ii), we get,

a = 2

Hence, the value of a and b are 2 and −1 respectively.