Question

Factor 4n^2 - 5n -6​

Answer 1

Answer:

(n-2) • (4n+3)

Step-by-step explanation:

4n2-5n-6  

Final result :

 (n - 2) • (4n + 3)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (22n2 -  5n) -  6

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  4n2-5n-6  

The first term is,  4n2  its coefficient is  4 .

The middle term is,  -5n  its coefficient is  -5 .

The last term, "the constant", is  -6  

Step-1 : Multiply the coefficient of the first term by the constant   4 • -6 = -24  

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

     -24    +    1    =    -23  

     -12    +    2    =    -10  

     -8    +    3    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3  

                    4n2 - 8n + 3n - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

                   4n • (n-2)

             Add up the last 2 terms, pulling out common factors :

                   3 • (n-2)

Step-5 : Add up the four terms of step 4 :

                   (4n+3)  •  (n-2)

            Which is the desired factorization

Final result :

 (n - 2) • (4n + 3)