Answer:
(x -8)(x +3) = 0
Step-by-step explanation:
When a quadratic has the factorization
(x +a)(x +b) = 0
It expands to
x² +(a+b)x +ab = 0
When you compare this expansion to the given quadratic, you find that the numbers "a" and "b" must satisfy the requirements ...
a+b = -5 . . . . . . the coefficient of the x term
ab = -24 . . . . . . the constant term
Another way to say this is that <em>you want to find two factors of -24 that have a sum of -5</em>.
___
At this point, you make use of your knowledge of signed numbers and of multiplication tables. You know that for the <em>product</em> of two numbers to be negative, exactly one of them must be negative. In order for the <em>sum</em> to be negative, the factor with the largest magnitude must be negative.
Here are the ways -24 can be factored with the largest (magnitude) factor negative:
-24 = -24×1 = -12×2 = -8×3 = -6×4
The sums of the factors in these factor pairs are -23, -10, -5, -2. The one we're interested in is -8×3 with a sum of (-8 +3) = -5.
It does not matter which number (-8 or 3) is assigned to a or to b. It only matters that we now know the factored equation is ...
(x -8)(x +3) = 0
