Answer:
(2x - 3)(x + 2)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
([tex]2x^{2}[/tex] + x) - 6
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring [tex]2x^{2}[/tex]+x-6
The first term is, [tex]2x^{2}[/tex] its coefficient is 2 .
The middle term is, +x its coefficient is 1 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 2 • -6 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is 1 .
-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1
-3 + 4 = 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 4
[tex]2x^{2}[/tex] - 3x + 4x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-3)
Add up the last 2 terms, pulling out common factors :
2 • (2x-3)
Step-5 : Add up the four terms of step 4 :
(x+2) • (2x-3)
Which is the desired factorization
(2x - 3)(x + 2)
