Question

10.Which of the following is HCF of 2x^2-18 and x^2-2x-3?

Answer 1

Answer: x - 3

Step-by-step 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.