Question

Question #e2e13

Answer 1

`x^2-3x-28=(x+4)(x-7) or (x-7)(x+4)` but they're both the same due to the Commutative Property of Multiplication.

Explanation:

To solve this problem, we need to identify an `a` and a `b` such that `ab=-28` and `a+b=-3`. Let's first list out the factors of 28 and see which ones add up to -3 (Ones that don't work = red; one that works = blue):

`color(red)(1 and 28)`

`color(red)(2 and 14)`

`color(blue)(4 and 7)`

We have found our pair! -4 and 7! So now, we need to write the original problem into a `(x+a)(x+b)` format. We have two ways of writing this:

Either `(x+4)(x-7)` or `(x-7)(x+4)` but they're both the same due to the Commutative Property of Multiplication.