is x-3 a factor of the polynomial p(x)=2x4-9x3+15x2-22x+12 and for waht reason

Yes, (x - 3) is a factor of the given polynomial.

If (x - 3) was a factor of the polynomial, then 3 would be one of the zeros of the function. That means if you input 3 into the function, you will get an output of zero.

In this case, inputting 3 does produce 0. Therefore, it is a factor.