Answer: x - 3
Explanation:
Factor:
2x^2 - 18
1. Factor out 2: 2(x^2 - 9)
2.Factor x^2 - 9 into (x-3)(x+3): 2(x - 3)(x + 3)
*Notice that x^2 - a^2 can always be factored into (x-a)(x+a)
where a is a constant so in this case, a is 9 which is also 3^2
so x^2 - 9 can be factored into (x - 3)(x + 3)
x^2 - 2x - 3
1. Think what two numbers multiplied together is -3 and added together is 2
-> 3 and -1 since 3(-1) = -3 and 3+ (-1) = 2
2. Factor x^2 - 2x -3 into (x - 3)(x + 1)
Therefore, since both 2x^2 - 18 and x^2 - 2x -3 do not have another common factor besides x - 3, x - 3 is the HCF of 2x^2 - 18 and x^2 - 2x -3.