Final answer:
The missing term in the factorization 12x2−75=3(2x?) (2x−5) is '+5', which completes the difference of squares factorization to 3(2x + 5) (2x - 5).
Step-by-step explanation:
To find the missing term in the factorization 12x2−75=3(2x?) (2x−5), we need to decompose the quadratic expression into factors. First, we can factor out the greatest common factor (GCF) of 3 from the left side of the equation, which gives us:
3(4x^2 - 25) = 3(2x?) (2x - 5)
Noticing that 4x^2 - 25 is a difference of squares and can be further factored into (2x + 5) (2x - 5), we can now rewrite the expression as:
3(2x + 5) (2x - 5) = 3(2x?) (2x - 5)
Comparing the two expressions, it's clear that the missing term denoted by '?' is +5. The factorization becomes:
12x^2 - 75 = 3(2x + 5) (2x - 5)