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 you want to find two factors of -24 that have a sum of -5.
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At this point, you make use of your knowledge of signed numbers and of multiplication tables. You know that for the product of two numbers to be negative, exactly one of them must be negative. In order for the sum 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
