(3x^2-11x-4)-(x-2)(2x+3)

(3x2-11x-4)-(x-2)(2x+3)

Final result :

 x2 - 10x + 2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((3•(x2))-11x)-4)-(x-2)•(2x+3)

Step  2  :

Equation at the end of step  2  :

 ((3x2 -  11x) -  4) -  (x - 2) • (2x + 3)

Step  3  :

Trying to factor by splitting the middle term

3.1     Factoring  x2-10x+2

The first term is,  x2  its coefficient is  1 .

The middle term is,  -10x  its coefficient is  -10 .

The last term, "the constant", is  +2

Step-1 : Multiply the coefficient of the first term by the constant   1 • 2 = 2

Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   -10 .

     -2    +    -1    =    -3

     -1    +    -2    =    -3

     1    +    2    =    3

     2    +    1    =    3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 x2 - 10x + 2

thus, the first answer choice, y = sec x, is the correct one