Question

split the middle term of 2x²-6x+4

Answer 1

Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2x2 - 6x) - 4 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :

2x2 - 6x - 4 = 2 • (x2 - 3x - 2)

Trying to factor by splitting the middle term
3.2 Factoring x2 - 3x - 2

The first term is, x2 its coefficient is 1 .
The middle term is, -3x its coefficient is -3 .
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 -3 .

-2 + 1 = -1
-1 + 2 = 1

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Equation at the end of step 3 :
2 • (x2 - 3x - 2) = 0
Step 4 :
Equations which are never true :
4.1 Solve : 2 = 0

Answer 2

2x^2 - 6x + 4 = 0
2x^2 - 4x - 2x + 4 = 0
2x^2 - 2x - 4x + 4 = 0
2x [ x - 1] - 4 [ x - 1 ] = 0
[ x - 1] [ 2x - 4 ] = 0
x - 1  = 0 or 2x - 4  = 0
x =1 or x = 4/2= 2.