Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((32•7x2) + 37x) - 40
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 63x2+37x-40
The first term is, 63x2 its coefficient is 63 .
The middle term is, +37x its coefficient is 37 .
The last term, "the constant", is -40
Step-1 : Multiply the coefficient of the first term by the constant 63 • -40 = -2520
Step-2 : Find two factors of -2520 whose sum equals the coefficient of the middle term, which is 37 .
| -2520 | + | 1 | = | -2519 | ||
| -1260 | + | 2 | = | -1258 | ||
| -840 | + | 3 | = | -837 | ||
| -630 | + | 4 | = | -626 | ||
| -504 | + | 5 | = | -499 | ||
| -420 | + | 6 | = | -414 | ||
| -360 | + | 7 | = | -353 | ||
| -315 | + | 8 | = | -307 | ||
| -280 | + | 9 | = | -271 | ||
| -252 | + | 10 | = | -242 | ||
| -210 | + | 12 | = | -198 | ||
| -180 | + | 14 | = | -166 | ||
| -168 | + | 15 | = | -153 | ||
| -140 | + | 18 | = | -122 | ||
| -126 | + | 20 | = | -106 | ||
| -120 | + | 21 | = | -99 | ||
| -105 | + | 24 | = | -81 | ||
| -90 | + | 28 | = | -62 | ||
| -84 | + | 30 | = | -54 | ||
| -72 | + | 35 | = | -37 | ||
| -70 | + | 36 | = | -34 | ||
| -63 | + | 40 | = | -23 | ||
| -60 | + | 42 | = | -18 | ||
| -56 | + | 45 | = | -11 | ||
| -45 | + | 56 | = | 11 | ||
| -42 | + | 60 | = | 18 | ||
| -40 | + | 63 | = | 23 | ||
| -36 | + | 70 | = | 34 | ||
| -35 | + | 72 | = | 37 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -35 and 72
63x2 - 35x + 72x - 40
Step-4 : Add up the first 2 terms, pulling out like factors :
7x • (9x-5)
Add up the last 2 terms, pulling out common factors :
8 • (9x-5)
Step-5 : Add up the four terms of step 4 :
(7x+8) • (9x-5)
Which is the desired factorization
Final result :
(9x - 5) • (7x + 8)
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