Answer: The factors of the given expressions are 3, (x-7) and (x-4).
Step-by-step explanation: We are given to find the factors of the following quadratic expression :
[tex]E=3x^2-33x+84~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the factors of the given expression, we need to find two integers with sum -33 and product 252.
From (i), we have
[tex]E\\\\=3x^2-33x+84\\\\=3x^2-21x-12x+84\\\\=3x(x-7)-12(x-7)\\\\=(x-7)(3x-12)\\\\=3(x-7)(x-4).[/tex]
Thus, the factors of the given expressions are 3, (x-7) and (x-4).
