Answer:
The common facor is x-3.
Step-by-step explanation:
The first expression can be factored with a difference of squares, x+3 and x-3. You can check that by multiplying them together to get x²-9. Knowing that you need a common factor, one that works for both expressions, you can immediately eliminate A and B. The second expression, x²-5x+6, has to share one of these two factors. To factor this, you find the numbers that multiply to the c term and add to the b term. (Ax²+bx+c) so b is -5 and c is 6. All you have to do is find out which two numbers add to -5 and multiply to 6. You start with factors of 6, which are +-6 and +-1, and +-3 and +-2. Say you try 6 and 1 first. The b term is negative, so these two added have to add to a negative number, which means positive 6 and positive 1 won´t work. The only way to add to -5 is to add 1 to -6 or -6 to 1, but multiplying those together gives you -6, and you need positive 6 in the c term. That leaves you with -2 and -3. they add to -5, and multiply to -6, which means that your common term is x-3. Test this by expanding your result, (x-2)(x-3), if you get the original expression theyre both factors.
