Question

Middle term splitting of 3x^2-2x-7

Answer 1

Step-by-step explanation:

3x2-2x-7=0 

Two solutions were found :

 x =(2-√88)/6=(1-√ 22 )/3= -1.230

 x =(2+√88)/6=(1+√ 22 )/3= 1.897

Step by step solution :

Step  1  :

Equation at the end of step  1  :

(3x2 - 2x) - 7 = 0

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3x2-2x-7 

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

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

The last term, "the constant", is  -7 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -7 = -21 

Step-2 : Find two factors of  -21  whose sum equals the coefficient of the middle term, which is   -2 .

     -21   +   1   =   -20     -7   +   3   =   -4     -3   +   7   =   4     -1   +   21   =   20

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored