Question

factorize 3x^2 + 2x - 6​

Answer 1

See the Answer Below Mate :-

                              $3x^2+2x-6$                      ...........(1)

We Will Factorize it By Quadratic Formula :-

=>Q·F·(Quadratic Formula) = B² - 4ac

Applying, the Quadratic Formula. We get:-

Where,  B = 2.                                                  [By the Equation no.1]

             A = 3.                                                   [By the Equation no.1]

           C = -6.                                                   [By the Equation no.1]

Putting, the values in the Formula :-

=>B² - 4ac

=>(2)² - 4(3)(-6)

=>4 - (-72)

=>4 + 72                                                             ...................[∵ -(-)=+]

=>76.                                                                 ...................[ANS]

Since, the discriminant is not a perfect square number, the quadratic will not factor.

Answer 2

Answer:

Explanation:

3x2-2x-6=0  

Two solutions were found :

x =(2-√76)/6=(1-√ 19 )/3= -1.120

x =(2+√76)/6=(1+√ 19 )/3= 1.786

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (3x2 -  2x) -  6  = 0  

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  3x2-2x-6  

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

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

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

Step-1 : Multiply the coefficient of the first term by the constant   3 • -6 = -18  

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -2 .

     -18    +    1    =    -17  

     -9    +    2    =    -7  

     -6    +    3    =    -3  

     -3    +    6    =    3  

     -2    +    9    =    7  

     -1    +    18    =    17  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored