Question

find a and b such that x square - 2 x minus 3 is a factor of the polynomial x cube minus 3 X square + a x minus b​

Answer 1

Here the principle involved is that a factor of a polynomial divides that polynomial exactly leaving a remainder of zero.

So here when we divide the factor with the polynomial, the remainder is in the form of (a+1)x + (b+3)=0. So when we equate (a+1) to zero we get the value of 'a' and when we equate (b+3) to zero we get the value of 'b'.