Answer: (2x - 5) • (4x - 1)
STEP 1 : Equation at the end of step 1
(23x2 - 22x) + 5
STEP 2 : Trying to factor by splitting the middle term
2.1 Factoring 8x2-22x+5
The first term is, 8x2 its coefficient is 8 .
The middle term is, -22x its coefficient is -22 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 8 • 5 = 40
Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is -22 .
-40 + -1 = -41
-20 + -2 = -22 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -2
8x2 - 20x - 2x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (2x-5)
Add up the last 2 terms, pulling out common factors :
1 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(4x-1) • (2x-5)
Which is the desired factorization
Final result : (2x - 5) • (4x - 1)