Answer:
((22•3n2) - 10n) + 2
STEP 1 :
Equation at the end of step 1
((22•3n2) - 10n) + 2
STEP 2 :
STEP 3 :
Pulling out like terms
3.1 Pull out like factors :
12n2 - 10n + 2 = 2 • (6n2 - 5n + 1)
Trying to factor by splitting the middle term
3.2 Factoring 6n2 - 5n + 1
The first term is, 6n2 its coefficient is 6 .
The middle term is, -5n its coefficient is -5 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 6 • 1 = 6
Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -5 .
-6 + -1 = -7
-3 + -2 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -2
6n2 - 3n - 2n - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
3n • (2n-1)
Add up the last 2 terms, pulling out common factors :
1 • (2n-1)
Step-5 : Add up the four terms of step 4 :
(3n-1) • (2n-1)
Which is the desired factorization
Final result :
2 • (2n - 1) • (3n - 1)
Explanation: