Answer:
3(x-8)(x+5)
Explanation:
You want to factor the quadratic 3x² -9x -120.
Common factor
Each of the coefficients is divisible by 3, so that is the first thing we can factor out:
= 3(x² -3x -40)
Quadratic factors
To factor the quadratic, we need factors of -40 that have a sum of -3.
-40 = -40(1) = -20(2) = -10(4) = -8(5)
The last of these factor pairs have a sum of -3, so the factorization is ...
= 3(x -8)(x +5)
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Additional comment
The product of factors (x+a) and (x+b) is ...
(x +a)(x +b) = x² +ax +bx +ab = x² +(a+b)x +ab
This is why we're looking for factors of -40 = ab, that have the sum (a+b) = -3.