Question

the following questions (Any two):
Find the factors of the Polynomial 3x2 - 2x - 1
​

Answer 1

Almora (Hindustani pronunciation: [əlmoːɽa]) is a municipal board and a cantonment town in the state of Uttarakhand, India. It is the administrative headquarters of Almora district.[4] Almora is located on a ridge at the southern edge of the Kumaon Hills of the Himalaya range, at a distance of 363 km (via NH9)[5] from the national capital New Delhi and 415 km via Saharanpur Rd, 351 km via NH109 and 388.6 km via Ambala- Dehradun- Haridwar Rd

Answer 2

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  

STEP

1

:

Equation at the end of step 1

 (3x2 -  2x) -  1

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  3x2-2x-1  

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  -1  

Step-1 : Multiply the coefficient of the first term by the constant   3 • -1 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -2 .

     -3    +    1    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  1  

                    3x2 - 3x + 1x - 1

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

                   3x • (x-1)

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

                    1 • (x-1)

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

                   (3x+1)  •  (x-1)

            Which is the desired factorization

Final result :

 (x - 1) • (3x + 1)