Answer: the correct option is (C) x - 1.
Step-by-step explanation: We are given to select the correct binomial that is a factor of the following trinomial :
[tex]T=4x^2+20x-24~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To select the factor, we need to factorize expression (i). To factorize, we need two integers with sum 20 and product -96.
From (i), we have
[tex]T\\\\=4x^2+20x-24\\\\=4x^2+24x-4x-24\\\\=4x(x+6)-4(x+6)\\\\=(x+6)(4x-4)\\\\=4(x+6)(x-1).[/tex]
So, the factors of the given trinomial are 4, (x + 6) and (x - 1).
Since 4 and ( x + 6) are not in the options, so (x - 1), is the correct binomial.
Thus, (C) is the correct option.
