Answer: The complete factorization of the given expression is \((x-2)(3x-4).\)
Step-by-step explanation: We are given to complete the factorization of the following quadratic expression :
\(E=3x^2-10x+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
To factorize the given expression, we need two integers with sum -10 and product 34. Those two integers are -6 and -4.
The factorization of expression (i) is as follows :
\(E\\\\=3x^2-10x+8\\\\=3x^2-6x-4x+8\\\\=3x(x-2)-4(x-2)\\\\=(x-2)(3x-4).\)
Thus, the complete factorization of the given expression is \((x-2)(3x-4).\)
