Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(52a2 - 35a) + 12
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 25a2-35a+12
The first term is, 25a2 its coefficient is 25 .
The middle term is, -35a its coefficient is -35 .
The last term, "the constant", is +12
Step-1 : Multiply the coefficient of the first term by the constant 25 • 12 = 300
Step-2 : Find two factors of 300 whose sum equals the coefficient of the middle term, which is -35 .
| -300 | + | -1 | = | -301 | ||
| -150 | + | -2 | = | -152 | ||
| -100 | + | -3 | = | -103 | ||
| -75 | + | -4 | = | -79 | ||
| -60 | + | -5 | = | -65 | ||
| -50 | + | -6 | = | -56 | ||
| -30 | + | -10 | = | -40 | ||
| -25 | + | -12 | = | -37 | ||
| -20 | + | -15 | = | -35 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -15
25a2 - 20a - 15a - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
5a • (5a-4)
Add up the last 2 terms, pulling out common factors :
3 • (5a-4)
Step-5 : Add up the four terms of step 4 :
(5a-3) • (5a-4)
Which is the desired factorization
Final result :
(5a - 4) • (5a - 3)
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