Question

Identify the factors of x2 − 4x − 21. (4 points)

(x − 7)(x + 3)

(x + 7)(x − 3)

(x + 21)(x − 1)

(x − 21)(x + 1)

Answer 1

(x-7)(x+3)

Explanation:

As the equation is :

`x^(2) -4x-21`

(If you are familliar with expansion rules of course) it can be said right away that -21 is a product of two numbers which add up to -4. It may not be intuitive right away but I think you will start seeing it with experience.

The most obvious factors are 7 and 3. Because we are dealing with a negative it would be -7 and 3 or 7 and -3.

Testing:

7-3=4 (Does not work)

-7+3=-4 (Does work)

So, the factors would be -7 and 3 and so the factorized form would be (x-7)(x+3).

Checking:

`(x-7)(x+3)=x^(2) +3x-7x-7(3)\\=x^(2)-4x-21`(Works, the answer is supposedly correct)

Hopefully my answer was useful, correct and understandable.

With Respect,

-I. B.