Hi Mukulu,

If all the polynomials have common factor, we can find the common factor(s) of the first two and use the remainder theorem to find the value of "a". If I look at 2x²-x-6 it can broken into factors of

2x²-x-6 = 2x²-4x+3x-6 = 2x(x-2)+3(x-2)=(2x+3)(x-2)

Since 2x²-x-6 has factors of (2x+3)& (x-2) we know it has roots at x=-3/2 & x=2 and the other two polynomials must at least one of these roots. So let's use the remainder theorem to find if x=-3/2 or x=2 are roots of 3x²-8x+4

f(-3/2)=3(-3/2)²-8(-3/2)+4= 22.75

f(2)=3(2)²-8(2)+4= 0

Since x=2 yields a remainder of 0 for 3x²-8x+4 we know that (x-2) is the only common factor for all of the polynomials. If you substitute x=2 into your last equation and set it equal to 0, you can solve for a using simple algebra.

Hope this helps,

Janice